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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

\frac{d}{d x} (2 x sin (x))

\frac{\partial}{\partial y} (sin (x^{3} y^{2}))

\frac{\partial}{\partial y} (3 x^{2} y^{4} - 4)

\frac{2}{x ^{2} + 3}

2 a x + b

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