The correct option is D xe^x e^x + c Let I = ∫ xe^x dx Using integration by parts, ∫ u.v dx=u∫ v dx ∫ ( dudx∫ v dx )dx I = xe^x ∫ ...

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Standard Formulae - 1

Evaluate ∫ ...

Question

Evaluate $\int x e^{x} d x$ .

- x e^{x} - e^{x} + c

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- x e^{x} + e^{x} + c

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x e^{x} + e^{x} + c

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x e^{x} - e^{x} + c

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Solution

The correct option is D $x e^{x} - e^{x} + c$
Let $I = \int x e^{x} d x$

Using integration by parts,
$\int u . v d x = u \int v d x$ $- \int (\frac{d u}{d x} \int v d x) d x$

$I = x e^{x} - \int 1 \cdot e^{x} d x$

$= x e^{x} - e^{x} + c$

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