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

The integral of (x/(x+2)+sqrt(x)) is x+2-2ln|x+2|+2/3 x^{3/2}+C

Popular >

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

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

x + 2 - 2 ln ∣ x + 2 ∣ + \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{x}{x + 2} d x + \int x d x

\int \frac{x}{x + 2} d x = x + 2 - 2 ln ∣ x + 2 ∣

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

= x + 2 - 2 ln ∣ x + 2 ∣ + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= x + 2 - 2 ln ∣ x + 2 ∣ + \frac{2}{3} x^{\frac{3}{2}} + C

\int \frac{8 ln ( x ^{2} )}{x} d x

\int \frac{7 x + 19}{( x - 3 ) ( x + 5 )} d x

\int \frac{5 x - 4}{x ^{2} + 12 x - 64} d x

\int 3 \frac{ln ( x )}{x ^{3}} d x

\int \frac{( e ^{2 x} )}{e ^{2 x} + 5} d x

What is the integral of (x/(x+2)+sqrt(x)) ?
The integral of (x/(x+2)+sqrt(x)) is x+2-2ln|x+2|+2/3 x^{3/2}+C