How do you find the antiderivative of $x^{2} \cdot e^{2 x}$ $x^2*e^(2x)$ ?

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Answer 1 · 2017-01-23T14:41:23

$= \frac{1}{2} e^{2 x} (x^{2} - x + \frac{1}{2}) + C$ $= 1/2 e^(2x) (x^2 - x + 1/2 ) + C$

$int x^2 e^(2x) dx = int x^2 (1/2 e^(2x))^prime dx$

$= 1/2 x^2 e^(2x) - int (x^2)^prime * 1/2 e^(2x) dx$

$= 1/2 x^2 e^(2x) - int x e^(2x) dx$

$= 1/2 x^2 e^(2x) - int x (1/2 e^(2x))^prime dx$

$= 1/2 x^2 e^(2x) - ( 1/2 x e^(2x) - int (x)^prime * 1/2 e^(2x) dx )$

$= 1/2 x^2 e^(2x) - 1/2 x e^(2x) + int 1/2 e^(2x) dx$

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

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

How do you find the antiderivative of x^2*e^(2x)x2⋅e2xx^2*e^(2x)?