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

The integral of x/(sin^2(x^2)) is -1/2 cot(x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Apply u-substitution

= \int \frac{1}{2 sin ^{2} ( u )} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} (- cot (u))

Substitute back

u = x^{2}

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

Simplify

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

Add a constant to the solution

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

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