What is the integral of 5arctan(x) ?

The integral of 5arctan(x) is 5(xarctan(x)-1/2 ln|x^2+1|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5arctan(x)

\int 5 arctan (x) d x

5 (x arctan (x) - \frac{1}{2} ln x^{2} + 1) + C

Solution steps

\int 5 arctan (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int arctan (x) d x

Apply Integration By Parts

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

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

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

= 5 (x arctan (x) - \frac{1}{2} ln x^{2} + 1)

Add a constant to the solution

= 5 (x arctan (x) - \frac{1}{2} ln x^{2} + 1) + C

\int sin (x) + yz e^{x z} d x

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

\int \frac{3 x}{x} d x

\int \frac{1 + a t ^{b}}{t ^{b}} d t

\int e^{x^{\frac{3}{2}}} d x

What is the integral of 5arctan(x) ?
The integral of 5arctan(x) is 5(xarctan(x)-1/2 ln|x^2+1|)+C