What is the integral of 1/(9+3x^2) ?

The integral of 1/(9+3x^2) is 1/(3sqrt(3))arctan(x/(sqrt(3)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(9+3x^2)

\int \frac{1}{9 + 3 x ^{2}} d x

\frac{1}{3 3} arctan (\frac{x}{3}) + C

Solution steps

\int \frac{1}{9 + 3 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{3 3 ( 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}{3 3} \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}{3 3} arctan (u)

Substitute back

u = \frac{3}{3} x

= \frac{1}{3 3} arctan (\frac{3}{3} x)

Simplify

\frac{1}{3 3} arctan (\frac{3}{3} x) : \frac{1}{3 3} arctan (\frac{x}{3})

= \frac{1}{3 3} arctan (\frac{x}{3})

Add a constant to the solution

= \frac{1}{3 3} arctan (\frac{x}{3}) + C

\int \frac{( x ^{3} + 1 )}{x ^{3} - 8} d x

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

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

\int (7 x^{6} + 9) x^{7} + 9 x d x

\int (- \frac{5 z}{2 z} - 9 z) d z

What is the integral of 1/(9+3x^2) ?
The integral of 1/(9+3x^2) is 1/(3sqrt(3))arctan(x/(sqrt(3)))+C