Show that - 1-1-x2 ex-1-xdx-ex-1-x-

I=∫ ( 1 1/x^2 )e^x+1/xdx. Substitute x+1/x=t. #160; ⇒ 1 1x^2dx=dt ∴ I=∫ e^tdt =e^t+C ⇒ I=e^x+1/x + C #160; ...

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Integration by Partial Fractions

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Question

Show that $\int (1 - \frac{1}{x^{2}}) e^{x + 1 / x} d x = e^{x + 1 / x} .$

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Solution

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