What is the integral of (arccot(e^x))/(e^x) ?

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

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integral of (arccot(e^x))/(e^x)

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

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

Solution steps

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

Apply Integration By Parts

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

= - \frac{arccot ( e ^{x} )}{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

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

Simplify

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

Add a constant to the solution

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

2 + \frac{4 ( s - 4 )}{s ^{2} + 16}

\frac{d}{d x} (- 3 sin (2 x))

g (t) = \frac{t - t}{t ^{\frac{1}{3}}}

\int \frac{e ^{x}}{e ^{x} + e ^{- x}} d x

n = 0 \sum \infty \frac{1}{2 ^{2^{n}}}

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