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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{d}{d x} (- 9 cot (x) csc (x))

\frac{d}{d x} (ln (\frac{3 + e ^{x}}{3 - e ^{x}}))

\frac{d}{d x} (a x^{4} + b x^{3} + c x^{2})

(3 x - 1)^{7} (2 x + 1)^{5}

\frac{d}{d y} (e^{2 y})

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