Sharedcv1.sagewsOpen in CoCalc
Cv1

Příklad 1

var("y")

y
(((3*x^2+5*x*y-2*y^2)*(x-y)^3)^2).show()
(3x2+5xy2y2)2(xy)6\displaystyle {\left(3 \, x^{2} + 5 \, x y - 2 \, y^{2}\right)}^{2} {\left(x - y\right)}^{6}
expand(_).show()
9x1024x9y32x8y2+172x7y3146x6y4188x5y5+484x4y6428x3y7+193x2y844xy9+4y10\displaystyle 9 \, x^{10} - 24 \, x^{9} y - 32 \, x^{8} y^{2} + 172 \, x^{7} y^{3} - 146 \, x^{6} y^{4} - 188 \, x^{5} y^{5} + 484 \, x^{4} y^{6} - 428 \, x^{3} y^{7} + 193 \, x^{2} y^{8} - 44 \, x y^{9} + 4 \, y^{10}
factor(_).show()
(3xy)2(x+2y)2(xy)6\displaystyle {\left(3 \, x - y\right)}^{2} {\left(x + 2 \, y\right)}^{2} {\left(x - y\right)}^{6}

Příklad 2

((x^2-1)/(3*x^3-11*x^2+13*x-5)).show()
x213x311x2+13x5\displaystyle \frac{x^{2} - 1}{3 \, x^{3} - 11 \, x^{2} + 13 \, x - 5}
(((x^2-1)/(3*x^3-11*x^2+13*x-5)).partial_fraction()).show()
43x51x1\displaystyle \frac{4}{3 \, x - 5} - \frac{1}{x - 1}

Příklad 3

integral(x^2*sin(x),x).show()
(x22)cos(x)+2xsin(x)\displaystyle -{\left(x^{2} - 2\right)} \cos\left(x\right) + 2 \, x \sin\left(x\right)
simplify.full?
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