What is the integral of sec^2(x)ln(tan(x)) ?

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

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integral of sec^2(x)ln(tan(x))

\int sec^{2} (x) ln (tan (x)) d x

ln (tan (x)) tan (x) - tan (x) + C

Solution steps

\int sec^{2} (x) ln (tan (x)) d x

Apply Integration By Parts

: ln (tan (x)) tan (x) - \int sec^{2} (x) d x

= ln (tan (x)) tan (x) - \int sec^{2} (x) d x

\int sec^{2} (x) d x = tan (x)

= ln (tan (x)) tan (x) - tan (x)

Add a constant to the solution

= ln (tan (x)) tan (x) - tan (x) + C

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