What is the integral of ((arctan(x))^5)/(x^2+1) ?

The integral of ((arctan(x))^5)/(x^2+1) is (arctan^6(x))/6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((arctan(x))^5)/(x^2+1)

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

\frac{arctan ^{6} ( x )}{6} + C

Solution steps

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = arctan (x)

= \frac{arctan ^{6} ( x )}{6}

Add a constant to the solution

= \frac{arctan ^{6} ( x )}{6} + C

\frac{d}{d x} ((x^{3} - 8)^{\frac{2}{3}})

x \to 3 - lim (x^{2} - 8)

\frac{\partial}{\partial x} (- e^{x} cos (y))

\int csc^{2} (5 t) d t

y = \frac{3}{x}, y = 12 x, y = \frac{x}{3}

What is the integral of ((arctan(x))^5)/(x^2+1) ?
The integral of ((arctan(x))^5)/(x^2+1) is (arctan^6(x))/6+C