What is the integral of (sec^2(x))/(tan^3(x)) ?

The integral of (sec^2(x))/(tan^3(x)) is -1/2 cot^2(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))/(tan^3(x))

\int \frac{sec ^{2} ( x )}{tan ^{3} ( x )} d x

- \frac{1}{2} cot^{2} (x) + C

Solution steps

\int \frac{sec ^{2} ( x )}{tan ^{3} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = tan (x)

= - \frac{1}{2 tan ^{2} ( x )}

Simplify

- \frac{1}{2 tan ^{2} ( x )} : - \frac{1}{2} cot^{2} (x)

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

Add a constant to the solution

= - \frac{1}{2} cot^{2} (x) + C

6 t \frac{d y}{d t} + y = t

3 x^{2} - 3

x^{5} sin (x)

x \to 0 lim (\frac{1 - cos ^{2} ( 3 x )}{x ^{2}})

f (x) = 3 arcsin (x^{4})

What is the integral of (sec^2(x))/(tan^3(x)) ?
The integral of (sec^2(x))/(tan^3(x)) is -1/2 cot^2(x)+C