What is the integral of cos^{-1}(x) ?

The integral of cos^{-1}(x) is xarccos(x)-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 cos^{-1}(x)

\int arccos (x) d x

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

Solution steps

\int arccos (x) d x

Apply Integration By Parts

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

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

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

= x arccos (x) - 1 - x^{2}

Add a constant to the solution

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

x^{2} + 9

\int_{1}^{5} \frac{x ^{2} + 8}{6 x - x ^{2}} d x

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

\int \frac{cot ^{2} ( x )}{cos ^{2} ( x )} d x

\frac{d}{d x} (\frac{1}{4} (e^{2 x} + e^{- 2 x}))

What is the integral of cos^{-1}(x) ?
The integral of cos^{-1}(x) is xarccos(x)-sqrt(1-x^2)+C