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