What is the integral of 3/(x^2+25) ?

The integral of 3/(x^2+25) is 3/5 arctan(x/5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/(x^2+25)

\int \frac{3}{x ^{2} + 25} d x

\frac{3}{5} arctan (\frac{x}{5}) + C

Solution steps

\int \frac{3}{x ^{2} + 25} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{x ^{2} + 25} d x

Apply Integral Substitution

= 3 \cdot \int \frac{1}{5 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 3 \cdot \frac{1}{5} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 3 \cdot \frac{1}{5} arctan (u)

Substitute back

u = \frac{x}{5}

= 3 \cdot \frac{1}{5} arctan (\frac{x}{5})

Simplify

3 \cdot \frac{1}{5} arctan (\frac{x}{5}) : \frac{3}{5} arctan (\frac{x}{5})

= \frac{3}{5} arctan (\frac{x}{5})

Add a constant to the solution

= \frac{3}{5} arctan (\frac{x}{5}) + C

\int (\frac{7}{3})^{x} d x

\int \frac{3 sin ( 2 x )}{sin ( x )} d x

\int 1 + 5^{2 x} d x

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

\int \frac{3}{4 x ^{2} + 1} d x

What is the integral of 3/(x^2+25) ?
The integral of 3/(x^2+25) is 3/5 arctan(x/5)+C