2911.sagews

var('z')
f=(z)
f.integral(z,0,1)

1/2

var ("y")
f= (y)
f. integral (y, 2,4)

6

var('y,a,b')
f=1/((a-b*y)^(1/2))
f.integral

-2*sqrt(-b*y + a)/b

var('x')
f= (5*x)+1^1/2
f. integral (x)

5/2*x^2 + x

var ('x')
f= 8*x/4*x^2+3^-1/6
f. integral(x)

1/2*x^4 + 1/18*x

var('y,a,b')
f=(a-b*y)^(-1/2)
f.integral (x)

x/sqrt(-b*y + a)

var ('z')
f= (6*z)/(5-3*z^2)^2
f.integral (z)

-1/(3*z^2 - 5)

var ('x,b,a')
f= (a+b*x)^(1/3)
f.integral (x)

3/4*(b*x + a)^(4/3)/b

integral(x*cos(x^2),x)

1/2*sin(x^2)

(1/(exp(x)+1)).integrate(x)

x - log(e^x + 1)

exp(-x^2).integrate(x)

1/2*sqrt(pi)*erf(x)

var ('r')
f= (r-10)/(r^3)
f.integral (r)

-(r - 5)/r^2

var ('x')
f= (3*x)^(3)-(4*x)^(2)+(3*x)/(x^2+1)
f.integral (x)

27/4*x^4 - 16/3*x^3 + 3/2*log(x^2 + 1)

var ('x')
f= 20+8*x-x^2
f. integral (x)

-1/3*x^3 + 4*x^2 + 20*x

var ('x')
f= (x^2+2)^3
f. integral (x)

1/7*x^7 + 6/5*x^5 + 4*x^3 + 8*x

var ('x')
f= 3^(7-2*(x))^3^1/2 (x)^2
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_14.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IDNeKDctMiooeCkpXjNeMS8yICh4KV4yCmYuaW50ZWdyYWwgKHgp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpjh9q1J/___code___.py", line 4, in <module> f= _sage_const_3 **(_sage_const_7 -_sage_const_2 *(x))**_sage_const_3 **_sage_const_1 /_sage_const_2 (x)**_sage_const_2 TypeError: 'sage.rings.integer.Integer' object is not callable

var ('x,a')
f= ((a)^1/2 - (x)^1/2)
f.integral (x)

1/2*a*x - 1/4*x^2

var ('x')
f= (x^2+1)/(x^3+3*x)^1/2
f.integral (x)

1/6*log(x^3 + 3*x)

var ('x,a')
f= (x^1/2)((a)^1/2-(x))^2
f.integral (x)

__main__:1: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) 1/16*a^2*x - 1/8*a*x^2 + 1/12*x^3

var ('t,a,d')
f= (t^3)/(a^4+t^4)^1/2
f.integral (t)

1/8*log(a^4 + t^4)

var ('x')
f= 3*cos (3*x)
f.integral(x)

sin(3*x)

var ('x')
f= sin(10*x)
f. integral (x)

-1/10*cos(10*x)

var ('x')
f= (sec^2) (1-4*x)
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_39.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IChzZWNeMikgKDEtNCp4KQpmLmludGVncmFsICh4KQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpD64LGw/___code___.py", line 4, in <module> f= (sec**_sage_const_2 ) (_sage_const_1 -_sage_const_4 *x) File "integer.pyx", line 1821, in sage.rings.integer.Integer.__pow__ (sage/rings/integer.c:12870) TypeError: unsupported operand type(s) for ** or pow(): 'Function_sec' and 'int'

var ('x')
f= (cos^4*x) (sen*x)
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_44.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IChjb3NeNCp4KSAoc2VuKngpCmYuaW50ZWdyYWwgKHgp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpBSPJhI/___code___.py", line 4, in <module> f= (cos**_sage_const_4 *x) (sen*x) File "integer.pyx", line 1821, in sage.rings.integer.Integer.__pow__ (sage/rings/integer.c:12870) TypeError: unsupported operand type(s) for ** or pow(): 'Function_cos' and 'int'

var ('x')
f= cos^2
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_47.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IChjb3NeMikKZi5pbnRlZ3JhbCAoeCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpF8xWMC/___code___.py", line 4, in <module> f= (cos**_sage_const_2 ) File "integer.pyx", line 1821, in sage.rings.integer.Integer.__pow__ (sage/rings/integer.c:12870) TypeError: unsupported operand type(s) for ** or pow(): 'Function_cos' and 'int'

var('s')
f= (3*s+4)^1/2
f.integral (s)

3/4*s^2 + 2*s

var ('x')
f= sin^2*x) (cos*x)
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_57.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IHNpbl4yKngpIChjb3MqeCkKZi5pbnRlZ3JhbCAoeCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpqJdVFi/___code___.py", line 4 f= sin**_sage_const_2 *x) (cos*x) ^ SyntaxError: invalid syntax

var ('x')
f= sec (5*x+1)
f.integral (x)

1/5*log(tan(5*x + 1) + sec(5*x + 1))

var ('x')
f= ((sen^5) (3*x) (cos3*x))
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_63.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9ICgoc2VuXjUpICgzKngpIChjb3MzKngpKQpmLmludGVncmFsICh4KQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpztrkbL/___code___.py", line 4, in <module> f= ((sen**_sage_const_5 ) (_sage_const_3 *x) (cos3*x)) NameError: name 'sen' is not defined

var ('x')
f= tan^2) (2*x) (sec^2) 2*x
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_74.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IHRhbl4yKSAoMip4KSAoc2VjXjIpIDIqeApmLmludGVncmFsICh4KQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpKBQdU4/___code___.py", line 4 f= tan**_sage_const_2 ) (_sage_const_2 *x) (sec**_sage_const_2 ) _sage_const_2 *x ^ SyntaxError: invalid syntax

var ('x')
f= (2)+(cos*x)/sen^2*x
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_76.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9ICgyKSsoY29zKngpL3Nlbl4yKngKZi5pbnRlZ3JhbCAoeCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpQocXno/___code___.py", line 4, in <module> f= (_sage_const_2 )+(cos*x)/sen**_sage_const_2 *x File "element.pyx", line 1459, in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:12096) File "coerce.pyx", line 766, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7337) TypeError: unsupported operand parent(s) for '*': '<class 'sage.functions.trig.Function_cos'>' and 'Symbolic Ring'

var('x')
f= x^2/x^3+5
f.integral (x)

5*x + log(x)

var ('x')
f= 1/x-7
f.integral (x)

-7*x + log(x)

var ('x')
f= (cos a*x/b+ sen a*x^1/2
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_82.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IChjb3MgYSp4L2IrIHNlbiBhKnheMS8yCmYuaW50ZWdyYWwgKHgp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpWD56WB/___code___.py", line 4 f= (cos a*x/b+ sen a*x**_sage_const_1 /_sage_const_2 ^ SyntaxError: invalid syntax

var('x')
f= (sec x/1+tan x)^1/2
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_83.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyKCd4JykKZj0gKHNlYyB4LzErdGFuIHgpXjEvMgpmLmludGVncmFsICh4KQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpGGvGES/___code___.py", line 4 f= (sec x/_sage_const_1 +tan x)**_sage_const_1 /_sage_const_2 ^ SyntaxError: invalid syntax

var ('t,d,a,b')
f= t*d*t/a+b*t^2
f.integral (t)

1/3*b*t^3 + 1/3*d*t^3/a

var ('x')
f= sin*x/1-cos*x
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_4.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IHNpbip4LzEtY29zKngKZi5pbnRlZ3JhbCAoeCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpmjSMT6/___code___.py", line 4, in <module> f= sin*x/_sage_const_1 -cos*x File "element.pyx", line 1459, in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:12096) File "coerce.pyx", line 766, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7337) TypeError: unsupported operand parent(s) for '*': '<class 'sage.functions.trig.Function_sin'>' and 'Symbolic Ring'

var ('x')
f= e^5*x
f.integral (x)

1/2*x^2*e^5

var ('x')
f= 1/1+e^-2*x
f.integral (x)

1/2*x^2*e^(-2) + x

var ('x')
f= e^4*x/x^2
f.integral (x)

e^4*log(x)

var ('x')
f= e^x/1+e^x^1/2
f.integral (x)

3/2*e^x

var ('x')
f= x^2/1-2*x^3
f.integral (x)

-1/2*x^4 + 1/3*x^3

var ('x')
f= x^3+5*x^2-4/x^2
f.integral (x)

1/4*x^4 + 5/3*x^3 + 4/x

var('x')
f= 1+tan*x^1/2
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_11.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyKCd4JykKZj0gMSt0YW4qeF4xLzIKZi5pbnRlZ3JhbCAoeCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpE_e9KH/___code___.py", line 4, in <module> f= _sage_const_1 +tan*x**_sage_const_1 /_sage_const_2 File "element.pyx", line 1459, in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:12096) File "coerce.pyx", line 766, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7337) TypeError: unsupported operand parent(s) for '*': '<class 'sage.functions.trig.Function_tan'>' and 'Symbolic Ring'

var ('x')
f= x^2 (x+1)^1/2
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_16.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IHheMiAoeCsxKV4xLzIKZi5pbnRlZ3JhbCAoeCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpuyAEBW/___code___.py", line 4, in <module> f= x**_sage_const_2 (x+_sage_const_1 )**_sage_const_1 /_sage_const_2 TypeError: 'sage.rings.integer.Integer' object is not callable

var('x')
f= 4*x(3*x^2+3)^1/2
f.integral (x)

2*x^3 + 6*x

var('x')
f= 3*x(2*-1)
f.integral (x)

-6*x

var('w')
f= (1-1/w) cos (w-lnw)
f.integral(w)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_20.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyKCd3JykKZj0gKDEtMS93KSBjb3MgKHctbG53KQpmLmludGVncmFsKHcp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpin97Mi/___code___.py", line 4 f= (_sage_const_1 -_sage_const_1 /w) cos (w-lnw) ^ SyntaxError: invalid syntax

var('y')
f= 3(8*y-1) e^4*y^2-y
f.integral (y)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_21.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyKCd5JykKZj0gMyg4KnktMSkgZV40KnleMi15CmYuaW50ZWdyYWwgKHkp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmp3VePtW/___code___.py", line 4 f= _sage_const_3 (_sage_const_8 *y-_sage_const_1 ) e**_sage_const_4 *y**_sage_const_2 -y ^ SyntaxError: invalid syntax

var('x')
f= 1/x+x^1/2
f.integral (x)

1/4*x^2 + log(x)

var ('x')
f= 3((7-2*x^3)^4)^1/2 x^2
f.integral (x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_24.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICgneCcpCmY9IDMoKDctMip4XjMpXjQpXjEvMiB4XjIKZi5pbnRlZ3JhbCAoeCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpwIffOz/___code___.py", line 4 f= _sage_const_3 ((_sage_const_7 -_sage_const_2 *x**_sage_const_3 )**_sage_const_4 )**_sage_const_1 /_sage_const_2 x**_sage_const_2 ^ SyntaxError: invalid syntax

var('x')
f= 1/5*x-2^1/2
f.integral (x)

1/10*x^2 - x

var ('x')
f= 1/x+1^1/2
f.integral (x)

1/2*x + log(x)

var('x')
f=x (x+1)^1/2
f.integral(x)

1/4*x^2 + 1/2*x