What is the integral of xsech^2(x) ?

The integral of xsech^2(x) is xtanh(x)-ln|cosh(x)|+C

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integral of xsech^2(x)

\int x sech^{2} (x) d x

x tanh (x) - ln ∣ cosh (x) ∣ + C

Solution steps

\int x sech^{2} (x) d x

Apply Integration By Parts

: x tanh (x) - \int tanh (x) d x

= x tanh (x) - \int tanh (x) d x

\int tanh (x) d x = ln ∣ cosh (x) ∣

= x tanh (x) - ln ∣ cosh (x) ∣

Add a constant to the solution

= x tanh (x) - ln ∣ cosh (x) ∣ + C

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What is the integral of xsech^2(x) ?
The integral of xsech^2(x) is xtanh(x)-ln|cosh(x)|+C