What is the integral of x/(sqrt(12-x^2)) ?

The integral of x/(sqrt(12-x^2)) is -sqrt(12-x^2)+C

Popular >

integral of x/(sqrt(12-x^2))

\int \frac{x}{12 - x ^{2}} d x

- 12 - x^{2} + C

Solution steps

\int \frac{x}{12 - x ^{2}} 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 = 12 - x^{2}

= - \frac{1}{2} \cdot 2 (12 - x^{2})^{\frac{1}{2}}

Simplify

- \frac{1}{2} \cdot 2 (12 - x^{2})^{\frac{1}{2}} : - 12 - x^{2}

= - 12 - x^{2}

Add a constant to the solution

= - 12 - x^{2} + C

\int \frac{1}{v ^{2}} 1 + \frac{1}{v} d v

\int \frac{sin ^{2} ( y )}{tan ^{4} ( y )} d y

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

\int \frac{2 ( 1 + x )}{27} d x

\int \frac{3 x ^{4} - 2 x ^{3} + x ^{2} - 10}{x ^{2} + 2} d x

What is the integral of x/(sqrt(12-x^2)) ?
The integral of x/(sqrt(12-x^2)) is -sqrt(12-x^2)+C