What is the integral of 1/(49x^2+1) ?

The integral of 1/(49x^2+1) is 1/7 arctan(7x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(49x^2+1)

\int \frac{1}{49 x ^{2} + 1} d x

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

Solution steps

\int \frac{1}{49 x ^{2} + 1} d x

Apply Integral Substitution

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

Substitute back

u = 7 x

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

Add a constant to the solution

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

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

\int \frac{x}{( x ^{2} + 2 ) 3 x ^{2} + 5} d x

\int 4 cos (2 t) d t

\int 4^{x} e^{x} d x

\int 24 x^{5} arctan (2 x^{3}) d x

What is the integral of 1/(49x^2+1) ?
The integral of 1/(49x^2+1) is 1/7 arctan(7x)+C