What is the integral of x/(sqrt(5x^2-3)) ?

The integral of x/(sqrt(5x^2-3)) is 1/5 sqrt(5x^2-3)+C

Popular >

integral of x/(sqrt(5x^2-3))

\int \frac{x}{5 x ^{2} - 3} d x

\frac{1}{5} 5 x^{2} - 3 + C

Solution steps

\int \frac{x}{5 x ^{2} - 3} 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} - 3

= \frac{1}{10} \cdot 2 (5 x^{2} - 3)^{\frac{1}{2}}

Simplify

\frac{1}{10} \cdot 2 (5 x^{2} - 3)^{\frac{1}{2}} : \frac{1}{5} 5 x^{2} - 3

= \frac{1}{5} 5 x^{2} - 3

Add a constant to the solution

= \frac{1}{5} 5 x^{2} - 3 + C

\int 3 t e^{- s t} d t

\int - sin (x) + e^{x} d x

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

\int \frac{5 x ^{3} + 9 x ^{2} - 22 x - 8}{x ^{3} - 4 x} d x

\int 2 x + sec^{2} (x) d x

What is the integral of x/(sqrt(5x^2-3)) ?
The integral of x/(sqrt(5x^2-3)) is 1/5 sqrt(5x^2-3)+C