How do you integrate $\int \frac{e^{\frac{1}{t}}}{t^{2}}$ $int e^(1/t)/t^2$ by parts?

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How do you integrate $\int \frac{e^{\frac{1}{t}}}{t^{2}}$ $int e^(1/t)/t^2$ by parts?

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Answer 1 · 2016-11-27T05:24:10

Integration by parts is a waste of time. Just use the substitution $u = \frac{1}{t}$ $u=1/t$ . This implies that $d u = - \frac{1}{t^{2}} d t$ $du=-1/t^2dt$ .

$\int \frac{e^{\frac{1}{t}}}{t^{2}} d t = - \int e^{\frac{1}{t}} \frac{- 1}{t^{2}} d t = - \int e^{u} d u = - e^{u} + C = - e^{\frac{1}{t}} + C$ $inte^(1/t)/t^2dt=-inte^(1/t)(-1)/t^2dt=-inte^udu=-e^u+C=-e^(1/t)+C$

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How do you integrate $\int \frac{e^{\frac{1}{t}}}{t^{2}}$ $int e^(1/t)/t^2$ by parts?

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