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

\frac{d}{d x} (\frac{x - 2}{x ^{2} + 5 x + 4})

\frac{d y}{d x} = - y^{\frac{1}{3}}

\frac{d ^{3}}{d x ^{3}} (e^{- x^{2}})

y = 2 x^{3}, y = 18 x

f (x) = 3 x - 2 x^{2}, (- 3, - 27)

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