What is the integral of x/(sqrt(5x^2+1)) ?

The integral of x/(sqrt(5x^2+1)) is 1/5 sqrt(5x^2+1)+C

Popular >

integral of x/(sqrt(5x^2+1))

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

\frac{1}{5} 5 x^{2} + 1 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{10 u} d u

= \int \frac{1}{10 u} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= \frac{1}{10} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 5 x^{2} + 1

= \frac{1}{10} \cdot 2 (5 x^{2} + 1)^{\frac{1}{2}}

Simplify

\frac{1}{10} \cdot 2 (5 x^{2} + 1)^{\frac{1}{2}} : \frac{1}{5} 5 x^{2} + 1

= \frac{1}{5} 5 x^{2} + 1

Add a constant to the solution

= \frac{1}{5} 5 x^{2} + 1 + C

\int sin (13 z) sin (9 z) d z

\int \frac{x}{2 x + 2} d x

\int (3 t^{4} + 2) t^{3} d t

\int \frac{x}{( x ^{2} + 4 ) ^{4}} d x

\int \frac{1}{x - \frac{1}{2}} d x

What is the integral of x/(sqrt(5x^2+1)) ?
The integral of x/(sqrt(5x^2+1)) is 1/5 sqrt(5x^2+1)+C