How do you find the integral of $x^5*e^(x^2)$ ?

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Answer 1 · 2018-04-25T10:50:16

$1/2x^4e^(x^2)-x^2e^(x^2)+e^(x^2)+C$

$intx^5*e^(x^2)dx$

$=1/2intx^4e^(x^2)*2xdx$

$=1/2intx^4e^(x^2)dx^2$

$x^2=u$

$d(x^2)=du$

$=1/2intx^4e^(x^2)dx^2=1/2intu^2e^udu$

$=1/2intu^2d(e^u)$

$=1/2(u^2e^u-int2ue^udu)$

$=1/2(u^2e^u-2intud(e^u))$

$=1/2(u^2e^u-2ue^u-(-2inte^udu))$

$=1/2u^2e^u-ue^u+e^u+C$

Reverse The Substitution

$=1/2x^4e^(x^2)-x^2e^(x^2)+e^(x^2)+C$

How do you find the integral of x^5*e^(x^2) x^5*e^(x^2) ?