What is the integral of 1/(4+7x^2) ?

The integral of 1/(4+7x^2) is 1/(2sqrt(7))arctan((sqrt(7))/2 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/(4+7x^2)

\int \frac{1}{4 + 7 x ^{2}} d x

\frac{1}{2 7} arctan (\frac{7}{2} x) + C

Solution steps

\int \frac{1}{4 + 7 x ^{2}} d x

Apply Integral Substitution

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2 7} arctan (u)

Substitute back

u = \frac{7}{2} x

= \frac{1}{2 7} arctan (\frac{7}{2} x)

Add a constant to the solution

= \frac{1}{2 7} arctan (\frac{7}{2} x) + C

\int \frac{x ^{3} + 4 x ^{2} + 2 x}{x ^{2} + 2} d x

\int 4 + x d x

\int t^{2} + 2 t - 15 d t

\int 4 - 6 x d x

\int x^{3} 13 + x^{4} d x

What is the integral of 1/(4+7x^2) ?
The integral of 1/(4+7x^2) is 1/(2sqrt(7))arctan((sqrt(7))/2 x)+C