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

The integral of (cos(x))/((1+sin^2(x))) is arctan(sin(x))+C

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

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

arctan (sin (x)) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{1 + u ^{2}} d u

= \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

\int \frac{1}{1 + u ^{2}} d u = arctan (u)

= arctan (u)

Substitute back

u = sin (x)

= arctan (sin (x))

Add a constant to the solution

= arctan (sin (x)) + C

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