What is the integral of (x-1)csc^2(2x-x^2) ?

The integral of (x-1)csc^2(2x-x^2) is 1/2 cot(2x-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 (x-1)csc^2(2x-x^2)

\int (x - 1) csc^{2} (2 x - x^{2}) d x

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

Solution steps

\int (x - 1) csc^{2} (2 x - 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 = 2 x - x^{2}

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

Simplify

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

Add a constant to the solution

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

\int (x + 4) e^{x} d x

\int sec^{14} (θ) tan (θ) d θ

\int x cos (b) x d x

\int \frac{2}{x 1 - x} d x

\int sin (x) + x cos (x) d x

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