What is the integral of (sec^2(x))/(csc^2(x)) ?

The integral of (sec^2(x))/(csc^2(x)) is -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 (sec^2(x))/(csc^2(x))

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

- x + tan (x) + C

Solution steps

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

Simplify

\frac{sec ^{2} ( x )}{csc ^{2} ( x )} : tan^{2} (x)

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

Rewrite using trig identities

= \int - 1 + sec^{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 1 d x + \int sec^{2} (x) d x

\int 1 d x = x

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

= - x + tan (x)

Add a constant to the solution

= - x + tan (x) + C

\int x csc^{2} (x) cot (x) d x

\int \frac{3 + sin ( x )}{cos ^{2} ( x )} d x

\int \frac{9 x ^{2} - 16}{x ^{3}} d x

\int 24 x d x

\int \frac{1}{- 8 x - x ^{2}} d x

What is the integral of (sec^2(x))/(csc^2(x)) ?
The integral of (sec^2(x))/(csc^2(x)) is -x+tan(x)+C