What is the integral of tan(x)ln(sec(x)) ?

The integral of tan(x)ln(sec(x)) is (ln^2(sec(x)))/2+C

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integral of tan(x)ln(sec(x))

\int tan (x) ln (sec (x)) d x

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

Solution steps

\int tan (x) ln (sec (x)) d x

Apply u-substitution

: \int \frac{ln ( u )}{u} d u

= \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{v ^{2}}{2}

Substitute back

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

Add a constant to the solution

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

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