1339.sagews

var('x')

x

diff( sin(x), x)

cos(x)

integrate(sin(x), x)

-cos(x)

f=(e^(2*x)*cos(x^2+1))/(log(arctan(x)))

f

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{e^{2 \, x} \cos\left(x^{2} + 1\right)}{\ln\left(\arctan\left(x\right)\right)}

a=diff(f, x)
a

\newcommand{\Bold}[1]{\mathbf{#1}}-2 \, \frac{x e^{2 \, x} \sin\left(x^{2} + 1\right)}{\ln\left(\arctan\left(x\right)\right)} + 2 \, \frac{e^{2 \, x} \cos\left(x^{2} + 1\right)}{\ln\left(\arctan\left(x\right)\right)} - \frac{e^{2 \, x} \cos\left(x^{2} + 1\right)}{{(x^{2} + 1)} \ln\left(\arctan\left(x\right)\right)^{2} \arctan\left(x\right)}

a.full_simplify()

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{(e^{2 \, x} \sin\left(1\right) \sin\left(x^{2}\right) - e^{2 \, x} \cos\left(1\right) \cos\left(x^{2}\right) - 2 \, {({(x^{3} \cos\left(1\right) + x^{2} \sin\left(1\right) + x \cos\left(1\right) + \sin\left(1\right))} e^{2 \, x} \sin\left(x^{2}\right) \arctan\left(x\right) + {(x^{3} \sin\left(1\right) - x^{2} \cos\left(1\right) + x \sin\left(1\right) - \cos\left(1\right))} e^{2 \, x} \cos\left(x^{2}\right) \arctan\left(x\right))} \ln\left(\arctan\left(x\right)\right))}}{{(x^{2} + 1)} \ln\left(\arctan\left(x\right)\right)^{2} \arctan\left(x\right)}

a.integrate(x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/jason3/193/code/16.py", line 6, in <module> exec compile(ur'a.integrate(x)' + '\n', '', 'single') File "", line 1, in <module> File "expression.pyx", line 5962, in sage.symbolic.expression.Expression.integral (sage/symbolic/expression.cpp:24542) File "/home/sage/sage_install/sage/local/lib/python2.6/site-packages/sage/calculus/calculus.py", line 563, in integral result = expression._maxima_().integrate(v) File "/home/sage/sage_install/sage/local/lib/python2.6/site-packages/sage/interfaces/maxima.py", line 1999, in integral return I(var) File "/home/sage/sage_install/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1390, in __call__ return self._obj.parent().function_call(self._name, [self._obj] + list(args), kwds) File "/home/sage/sage_install/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1298, in function_call return self.new(s) File "/home/sage/sage_install/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1094, in new return self(code) File "/home/sage/sage_install/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1029, in __call__ return cls(self, x, name=name) File "/home/sage/sage_install/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1433, in __init__ raise TypeError, x TypeError: Computation failed since Maxima requested additional constraints (try the command 'assume(x>0)' before integral or limit evaluation, for example): Is x positive or negative?