What is the integral of x^2*arccos(x) ?

The integral of x^2*arccos(x) is 1/3 x^3arccos(x)+1/3 (1/3 (1-x^2)^{3/2}-sqrt(1-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^2*arccos(x)

\int x^{2} \cdot arccos (x) d x

\frac{1}{3} x^{3} arccos (x) + \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} arccos (x) - \int - \frac{x ^{3}}{3 1 - x ^{2}} d x

= \frac{1}{3} x^{3} arccos (x) - \int - \frac{x ^{3}}{3 1 - x ^{2}} d x

\int - \frac{x ^{3}}{3 1 - x ^{2}} d x = - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

= \frac{1}{3} x^{3} arccos (x) - (- \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}))

Simplify

= \frac{1}{3} x^{3} arccos (x) + \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

Add a constant to the solution

= \frac{1}{3} x^{3} arccos (x) + \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

\int \frac{1}{1 + cot ( x )} d x

\int tan^{11} (x) sec^{2} (x) d x

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

rr (θ) 2 - 4 sin (θ)

\int x^{2} (x - 3) d x

What is the integral of x^2*arccos(x) ?
The integral of x^2*arccos(x) is 1/3 x^3arccos(x)+1/3 (1/3 (1-x^2)^{3/2}-sqrt(1-x^2))+C