What is the integral of 1/(sin^2(a)x) ?

The integral of 1/(sin^2(a)x) is csc^2(a)ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(sin^2(a)x)

\int \frac{1}{sin ^{2} ( a ) x} d x

csc^{2} (a) ln ∣ x ∣ + C

Solution steps

\int \frac{1}{sin ^{2} ( a ) x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{sin ^{2} ( a )} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{sin ^{2} ( a )} ln ∣ x ∣

Use the basic trigonometric identity:

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

= csc^{2} (a) ln ∣ x ∣

Add a constant to the solution

= csc^{2} (a) ln ∣ x ∣ + C

5 x - 2 x

y^{^{'}} = x^{5} + 2 x^{4} - x - 2

t^{\frac{1}{2}}

n = 1 \sum \infty \frac{5 ^{n}}{n}

y^{^{''}} - 8 y^{^{'}} + 25 y = 5 x^{3} e^{- x} - 7 e^{- x}

What is the integral of 1/(sin^2(a)x) ?
The integral of 1/(sin^2(a)x) is csc^2(a)ln|x|+C