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

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

Popular >

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

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

- - x^{2} - 4 x + C

Solution steps

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

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

Simplify

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

= - - x^{2} - 4 x

Add a constant to the solution

= - - x^{2} - 4 x + C

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

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

\int x (1 - x^{2})^{10} d x

\int 6 x e^{- \frac{x}{6}} d x

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

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