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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

arctan (sin (x)) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

= arctan (u)

Substitute back

u = sin (x)

= arctan (sin (x))

Add a constant to the solution

= arctan (sin (x)) + C

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

\int sec^{2} (\frac{x}{2}) tan (\frac{x}{2}) d x

\int (- 6 x^{2} + 2 x) sin (x) d x

\int \frac{cos ( \frac{π}{x ^{29}} )}{x ^{30}} d x

\int \frac{1}{e ^{x} ( - e ^{- x} + 1 )} d x

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