∫ e^x (1x 1x^2)dx Using by parts, u = 1x , v = e^x du = 1x^2 , ∫ v dv = e^x #160; e^xx + ∫e^xx^2dx ∫e^xx^2dx e^xx + C ...

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Integration by Parts

∫ exx-1x2dx.

Question

$\int e^{x} (\frac{x - 1}{x^{2}}) d x$ .

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Solution

$\int e^{x} (\frac{1}{x} - \frac{1}{x^{2}}) d x$
Using by parts,
$u = \frac{1}{x}, v = e^{x}$
$d u = - \frac{1}{x^{2}}, \int v d v = e^{x}$
$\frac{e^{x}}{x} + \int \frac{e^{x}}{x^{2}} d x - \int \frac{e^{x}}{x^{2}} d x$
$\frac{e^{x}}{x} + C$

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