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

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

Popular >

integral of x/(sqrt(x^2+3))

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

x^{2} + 3 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

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

Substitute back

u = x^{2} + 3

= \frac{1}{2} \cdot 2 (x^{2} + 3)^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (x^{2} + 3)^{\frac{1}{2}} : x^{2} + 3

= x^{2} + 3

Add a constant to the solution

= x^{2} + 3 + C

\frac{\partial}{\partial x} (tan (ln (x \cdot y)))

\frac{d}{d x} (cos (e^{3 x^{2}}))

\int (1 + x)^{4} d x

\int - 2 x^{2} d x

\int_{\frac{7}{6}}^{6} \frac{1}{1 - x ^{2}} d x

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