Integration hard sum!

\int \frac{arc tan(e^{x})}{e^x}dx

3 Answers

21
tapanmast Vora ·

let ex = t

I = ∫(tan-1u)/u2

now do by parts takin (tan-1u) as da diff. functn. then its very easy

[1]

39
Dr.House ·

even take \large \tan^{-1} e^{x}=t

and proceed. thats another way.

in the end u will get I= \large \int t\sec ^{2}t dt +\int t dt

39
Dr.House ·

first one int by parts, and second one i need not tell u

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