What is the integral of (tan(y))/(sin^2(y)) ?

The integral of (tan(y))/(sin^2(y)) is ln|tan(y)|+C

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integral of (tan(y))/(sin^2(y))

\int \frac{tan ( y )}{sin ^{2} ( y )} d y

ln ∣ tan (y) ∣ + C

Solution steps

\int \frac{tan ( y )}{sin ^{2} ( y )} d y

Rewrite using trig identities

= \int \frac{sec ( y )}{sin ( y )} d y

Apply Trigonometric 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 = tan (y)

= ln ∣ tan (y) ∣

Add a constant to the solution

= ln ∣ tan (y) ∣ + C

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What is the integral of (tan(y))/(sin^2(y)) ?
The integral of (tan(y))/(sin^2(y)) is ln|tan(y)|+C