What is the integral of csc(x)cos(x) ?

The integral of csc(x)cos(x) is ln|sin(x)|+C

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integral of csc(x)cos(x)

\int csc (x) cos (x) d x

ln ∣ sin (x) ∣ + C

Solution steps

\int csc (x) cos (x) d x

Rewrite using trig identities

= \int \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sin (x)

= ln ∣ sin (x) ∣

Add a constant to the solution

= ln ∣ sin (x) ∣ + C

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What is the integral of csc(x)cos(x) ?
The integral of csc(x)cos(x) is ln|sin(x)|+C