What is the integral of e^{-x}*arccot(e^x) ?

The integral of e^{-x}*arccot(e^x) is -e^{-x}arccot(e^x)+1/2 ln|e^{2x}+1|-x+C

Popular >

integral of e^{-x}*arccot(e^x)

\int e^{- x} \cdot arccot (e^{x}) d x

- e^{- x} arccot (e^{x}) + \frac{1}{2} ln e^{2 x} + 1 - x + C

Solution steps

\int e^{- x} arccot (e^{x}) d x

Apply Integration By Parts

: - e^{- x} arccot (e^{x}) - \int \frac{1}{e ^{2 x} + 1} d x

= - e^{- x} arccot (e^{x}) - \int \frac{1}{e ^{2 x} + 1} d x

\int \frac{1}{e ^{2 x} + 1} d x = - \frac{1}{2} ln e^{2 x} + 1 + x

= - e^{- x} arccot (e^{x}) - (- \frac{1}{2} ln e^{2 x} + 1 + x)

Simplify

= - e^{- x} arccot (e^{x}) + \frac{1}{2} ln e^{2 x} + 1 - x

Add a constant to the solution

= - e^{- x} arccot (e^{x}) + \frac{1}{2} ln e^{2 x} + 1 - x + C

\int x^{2} (x^{3} - 1)^{5} d x

\int \frac{9 x}{4 + x ^{4}} d x

\int 2 x^{3} y^{4} + x d x

\int \frac{2 x ^{2} + 1}{x ^{2} ( 1 + x ^{2} )} d x

\int \frac{4 y}{1 + y ^{2}} d y

What is the integral of e^{-x}*arccot(e^x) ?
The integral of e^{-x}*arccot(e^x) is -e^{-x}arccot(e^x)+1/2 ln|e^{2x}+1|-x+C