What is the integral of (ln(tan(x)))/(sin(x)*cos(x)) ?

The integral of (ln(tan(x)))/(sin(x)*cos(x)) is (ln^2(tan(x)))/2+C

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integral of (ln(tan(x)))/(sin(x)*cos(x))

\int \frac{ln ( tan ( x ) )}{sin ( x ) \cdot cos ( x )} d x

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

Solution steps

\int \frac{ln ( tan ( x ) )}{sin ( x ) cos ( x )} d x

Apply Trigonometric Substitution

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

Apply u-substitution

= \int v d v

Apply the Power Rule

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

Substitute back

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

Add a constant to the solution

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

\int 2 (1 + x - 1)^{3} d x

\int x sin (x) - x d x

\int - \frac{1}{y ^{3}} d y

\int \frac{1}{T ^{2}} d T

\int x e^{- (\frac{x}{2})^{2}} d x

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