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Popular >

integral of cot(z)ln(sin(z))

Solution

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

Solution

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

Solution steps

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

Rewrite using trig identities

= \int cos (z) ln (sin (z)) csc (z) d z

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 ( z ) )}{2}

Add a constant to the solution

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

Popular Examples

integral of (32)/(x^4+16)

\int \frac{32}{x ^{4} + 16} d x

integral of sin^4(5x)cos^5(5x)

\int sin^{4} (5 x) cos^{5} (5 x) d x

integral of 1/((4x^2-4x+27)^{3/2)}

\int \frac{1}{( 4 x ^{2} - 4 x + 27 ) ^{\frac{3}{2}}} d x

integral of ((x))/(1+x^2)

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

integral of e^{6x}cos(e^{3x})

\int e^{6 x} cos (e^{3 x}) d x

Frequently Asked Questions (FAQ)

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