2∫ x ^ 2 e ^ x ^ 2 dx =2[ x ^ 2 ∫ e ^ x ^ 2 dx +∫ d dx x ^ 2 . ∫ e ^ x ^ 2 dx #160; ] dx (integration by parts) = 2 x ^ 2 e ^ x ^ 2 2x ...

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Integration by Parts

Integrate: 2...

Question

Integrate:
$2 x^{2} e^{x^{2}}$

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Solution

$2 \int x^{2} e^{x^{2}} d x = 2 [x^{2} \int e^{x^{2}} d x + \int \frac{d}{d x} x^{2} . \int e^{x^{2}} d x] d x (i n t e g r a t i o n b y p a r t s) = \frac{2 x^{2} e^{x^{2}}}{2 x} + 2 \int 2 x . \frac{e^{x^{2}}}{2 x} d x = x e^{x^{2}} + \frac{2. e^{x^{2}}}{2 x} + C = (\frac{x^{2} + 1}{x}) e^{x^{2}} + C$

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