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

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

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integral of cos(x)csc(x)

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

ln ∣ sin (x) ∣ + C

Solution steps

\int cos (x) csc (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

\frac{d}{d x} (x^{2} \cdot f (x))

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

\frac{x}{6 x - 6}

\frac{d}{d x} (∣ x ∣^{3})

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

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