What is the integral of (1/(7+7x^2)) ?

The integral of (1/(7+7x^2)) is 1/7 arctan(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1/(7+7x^2))

\int (\frac{1}{7 + 7 x ^{2}}) d x

\frac{1}{7} arctan (x) + C

Solution steps

\int \frac{1}{7 + 7 x ^{2}} d x

\frac{1}{7 + 7 x ^{2}} = \frac{1}{7} \frac{1}{1 + x ^{2}}

= \int \frac{1}{7} \cdot \frac{1}{1 + x ^{2}} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{1}{1 + x ^{2}} d x

Use the common integral:

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

= \frac{1}{7} arctan (x)

Add a constant to the solution

= \frac{1}{7} arctan (x) + C

\int t^{3} cos (t) d t

\int \frac{1 + e ^{2 x}}{4 e ^{x}} d x

\int cos (x) d \frac{1}{x} d x

\int x^{2} \cdot x^{3} - 5 d x

\int \frac{x ^{3}}{x ^{2} + 10} d x

What is the integral of (1/(7+7x^2)) ?
The integral of (1/(7+7x^2)) is 1/7 arctan(x)+C