What is the integral of tanh(x)ln(cosh(x)) ?

The integral of tanh(x)ln(cosh(x)) is (ln^2(cosh(x)))/2+C

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integral of tanh(x)ln(cosh(x))

\int tanh (x) ln (cosh (x)) d x

\frac{ln ^{2} ( cosh ( x ) )}{2} + C

Solution steps

\int tanh (x) ln (cosh (x)) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = ln (cosh (x))

= \frac{ln ^{2} ( cosh ( x ) )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( cosh ( x ) )}{2} + C

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What is the integral of tanh(x)ln(cosh(x)) ?
The integral of tanh(x)ln(cosh(x)) is (ln^2(cosh(x)))/2+C