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

The integral of (cos(2x))/(sin^2(x)cos^2(x)) is -cot(x)-tan(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(2x))/(sin^2(x)cos^2(x))

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

- cot (x) - tan (x) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{cos ^{2} ( x ) - sin ^{2} ( x )}{cos ^{2} ( x ) sin ^{2} ( x )} d x

Expand

\frac{cos ^{2} ( x ) - sin ^{2} ( x )}{cos ^{2} ( x ) sin ^{2} ( x )} : \frac{1}{sin ^{2} ( x )} - \frac{1}{cos ^{2} ( x )}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{sin ^{2} ( x )} d x = - cot (x)

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

= - cot (x) - tan (x)

Add a constant to the solution

= - cot (x) - tan (x) + C

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

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

\int \frac{1}{x ^{2} + 2 x + 4} d x

\int cos (x) cos (\frac{x}{2}) d x

\int \frac{4 x ^{3} - 3 x}{x ^{4} - 2 x ^{2} + 5} d x

What is the integral of (cos(2x))/(sin^2(x)cos^2(x)) ?
The integral of (cos(2x))/(sin^2(x)cos^2(x)) is -cot(x)-tan(x)+C