What is the integral of (cot(x))ln(sin(x)) ?

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

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integral of (cot(x))ln(sin(x))

\int (cot (x)) ln (sin (x)) d x

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

Solution steps

\int cot (x) ln (sin (x)) d x

Rewrite using trig identities

= \int cos (x) ln (sin (x)) csc (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} ( sin ( x ) )}{2}

Add a constant to the solution

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

\int \frac{x ^{3} + 4 x ^{2} - 4 x - 1}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{x ^{2} + 31}{x ^{2} + 36} d x

\int 6 x e^{0.005 x^{2}} d x

\int \frac{1}{x ^{2} - 6 x - 7} d x

\frac{1}{sec ^{2} ( x )}

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