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

The integral of (x+2)sqrt(x+4) is 2/3 (x+2)(x+4)^{3/2}-4/15 (x+4)^{5/2}+C

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integral of (x+2)sqrt(x+4)

\int (x + 2) x + 4 d x

\frac{2}{3} (x + 2) (x + 4)^{\frac{3}{2}} - \frac{4}{15} (x + 4)^{\frac{5}{2}} + C

Solution steps

\int (x + 2) x + 4 d x

Apply Integration By Parts

: \frac{2}{3} (x + 2) (x + 4)^{\frac{3}{2}} - \int \frac{2}{3} (x + 4)^{\frac{3}{2}} d x

= \frac{2}{3} (x + 2) (x + 4)^{\frac{3}{2}} - \int \frac{2}{3} (x + 4)^{\frac{3}{2}} d x

\int \frac{2}{3} (x + 4)^{\frac{3}{2}} d x = \frac{4}{15} (x + 4)^{\frac{5}{2}}

= \frac{2}{3} (x + 2) (x + 4)^{\frac{3}{2}} - \frac{4}{15} (x + 4)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} (x + 2) (x + 4)^{\frac{3}{2}} - \frac{4}{15} (x + 4)^{\frac{5}{2}} + C

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What is the integral of (x+2)sqrt(x+4) ?
The integral of (x+2)sqrt(x+4) is 2/3 (x+2)(x+4)^{3/2}-4/15 (x+4)^{5/2}+C