What is the integral of (ln(cos(x)))/(cot(x)) ?

The integral of (ln(cos(x)))/(cot(x)) is -(ln^2(cos(x)))/2+C

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integral of (ln(cos(x)))/(cot(x))

\int \frac{ln ( cos ( x ) )}{cot ( x )} d x

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

Solution steps

\int \frac{ln ( cos ( x ) )}{cot ( x )} d x

Use the basic trigonometric identity:

\frac{1}{cot ( x )} = tan (x)

= \int ln (cos (x)) tan (x) d x

Apply u-substitution

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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} ( cos ( x ) )}{2}

Add a constant to the solution

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

\int (3 x - 4)^{4} d x

7 t

f (x) = 3 25 - x^{2}

\frac{d}{d x} (\frac{c ^{3} - x ^{3}}{c ^{3} + x ^{3}})

\int \frac{8}{x x ^{2} + 2} d x

What is the integral of (ln(cos(x)))/(cot(x)) ?
The integral of (ln(cos(x)))/(cot(x)) is -(ln^2(cos(x)))/2+C