Ukol1c.sagews

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<h1>
    Ukol 1
</h1>

Priklad 1

reset()

%typeset_mode True

var('x,y')

($\displaystyle x$, $\displaystyle y$)

a=(((3*x^2+5*x*y-2*y^2)*(x-y)^3)^2);a

$\displaystyle {\left(3 \, x^{2} + 5 \, x y - 2 \, y^{2}\right)}^{2} {\left(x - y\right)}^{6}$

b=expand(a);b

$\displaystyle 9 \, x^{10} - 24 \, x^{9} y - 32 \, x^{8} y^{2} + 172 \, x^{7} y^{3} - 146 \, x^{6} y^{4} - 188 \, x^{5} y^{5} + 484 \, x^{4} y^{6} - 428 \, x^{3} y^{7} + 193 \, x^{2} y^{8} - 44 \, x y^{9} + 4 \, y^{10}$

c=factor(a);c

$\displaystyle {\left(3 \, x - y\right)}^{2} {\left(x + 2 \, y\right)}^{2} {\left(x - y\right)}^{6}$

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<h1>
    Ukol 2
</h1>

Priklad 2

reset()

a=((x^2-1)/(3*x^3-11*x^2+13*x-5)); a

$\displaystyle \frac{x^{2} - 1}{3 \, x^{3} - 11 \, x^{2} + 13 \, x - 5}$

b=(a).partial_fraction(); b

$\displaystyle \frac{4}{3 \, x - 5} - \frac{1}{x - 1}$

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<h1>
    Ukol 3
</h1>

reset()

a=integrate(x^2*sin(x), x); a

$\displaystyle -{\left(x^{2} - 2\right)} \cos\left(x\right) + 2 \, x \sin\left(x\right)$