What is the integral of xcsc^2(x^2) ?

The integral of xcsc^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

Popular >

integral of xcsc^2(x^2)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{csc ^{2} ( u )}{2} d u

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

Use the common integral:

\int csc^{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

\int \frac{1}{2 + 5 cos ( x )} d x

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

\int (5 x - 3)^{3} d x

\int t sin (t) d t

\int - 2 t^{4} e^{6 t^{5}} d t

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