What is the integral of cot(x)(2+ln(sin(x))) ?

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

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integral of cot(x)(2+ln(sin(x)))

\int cot (x) (2 + ln (sin (x))) d x

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

Solution steps

\int cot (x) (2 + ln (sin (x))) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = 2 + ln (sin (x))

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

Add a constant to the solution

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

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