∫(e^xx^2 e^2x)dx #10; #10; =∫e^xx^2dx #160; ∫e^2xdx #10; #10; = #160; x^2e^x ∫2xe^x dx #10;e^2x 2 + C #10; #10; =x ...

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Combination

Solve: ∫exx...

Question

Solve: $\int e^{x} x^{2} - e^{2 x} d x$

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Solution

$\int (e^{x} x^{2} - e^{2 x}) d x$

$= \int e^{x} x^{2} d x - \int e^{2 x} d x$

$= x^{2} e^{x} - \int 2 x e^{x} d x - \frac{e^{2 x}}{2} + C$

$= x^{2} e^{x} - 2 [x e^{x} - \int 1. e^{x} d x] - \frac{1}{2} e^{2 x} + C$

$= x^{2} e^{x} - 2 x e^{x} + 2 e^{x} - \frac{e^{2 x}}{2} + C$

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