What is the integral of (sin(2x))/(sin^2(x)+1) ?

The integral of (sin(2x))/(sin^2(x)+1) is ln|sin^2(x)+1|+C

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integral of (sin(2x))/(sin^2(x)+1)

\int \frac{sin ( 2 x )}{sin ^{2} ( x ) + 1} d x

ln sin^{2} (x) + 1 + C

Solution steps

\int \frac{sin ( 2 x )}{sin ^{2} ( x ) + 1} 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^{2} (x) + 1

= ln sin^{2} (x) + 1

Add a constant to the solution

= ln sin^{2} (x) + 1 + C

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What is the integral of (sin(2x))/(sin^2(x)+1) ?
The integral of (sin(2x))/(sin^2(x)+1) is ln|sin^2(x)+1|+C