What is the integral of (cos(a)x)/(sin^5(a)x) ?

The integral of (cos(a)x)/(sin^5(a)x) is xcsc^5(a)cos(a)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (cos(a)x)/(sin^5(a)x)

\int \frac{cos ( a ) x}{sin ^{5} ( a ) x} d x

x csc^{5} (a) cos (a) + C

Solution steps

\int \frac{cos ( a ) x}{sin ^{5} ( a ) x} d x

Simplify

\frac{cos ( a ) x}{sin ^{5} ( a ) x} : \frac{1}{sin ^{5} ( a )} cos (a)

= \int \frac{1}{sin ^{5} ( a )} cos (a) d x

Integral of a constant:

\int a d x = a x

= \frac{1}{sin ^{5} ( a )} cos (a) x

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= x csc^{5} (a) cos (a)

Add a constant to the solution

= x csc^{5} (a) cos (a) + C

What is the integral of (cos(a)x)/(sin^5(a)x) ?
The integral of (cos(a)x)/(sin^5(a)x) is xcsc^5(a)cos(a)+C