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

The integral of x/(sqrt(2^2-x^2)) is -sqrt(4-x^2)+C

Popular >

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

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

- 4 - x^{2} + C

Solution steps

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

Simplify

= \int \frac{x}{4 - 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 = 4 - x^{2}

= - \frac{1}{2} \cdot 2 (4 - x^{2})^{\frac{1}{2}}

Simplify

- \frac{1}{2} \cdot 2 (4 - x^{2})^{\frac{1}{2}} : - 4 - x^{2}

= - 4 - x^{2}

Add a constant to the solution

= - 4 - x^{2} + C

\int \frac{x}{( 64 + x ^{2} ) ^{3}} d x

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

\int e^{2 θ} cos (4 θ) d θ

\int \frac{x ^{2} + 3 x + 1}{( x - 1 ) ( x - 2 ) ( x - 3 )} d x

\int \frac{x}{x ^{2} - 7 x + 13} d x

What is the integral of x/(sqrt(2^2-x^2)) ?
The integral of x/(sqrt(2^2-x^2)) is -sqrt(4-x^2)+C