What is the integral of (x+3)/(sqrt(x+2)) ?

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

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integral of (x+3)/(sqrt(x+2))

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

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

Solution steps

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

Apply Integration By Parts

: 2 (x + 3) x + 2 - \int 2 x + 2 d x

= 2 (x + 3) x + 2 - \int 2 x + 2 d x

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

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

Add a constant to the solution

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

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