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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

= \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} ( tan ( x ) )}{2}

Add a constant to the solution

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

\int \frac{arctan ( x )}{x ^{2} ( 1 + x ^{2} )} d x

\int (x + e^{x}) x d x

\int \frac{1}{4 + 25 x ^{2}} d x

\int \frac{x cos ( x )}{sin ^{3} ( x )} d x

\int \frac{3}{x ^{2} + 3 x} 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