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

The integral of x/(sqrt(2x+2)) is xsqrt(2x+2)-1/3 (2x+2)^{3/2}+C

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

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

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

Solution steps

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

Apply Integration By Parts

: x 2 x + 2 - \int 2 x + 2 d x

= x 2 x + 2 - \int 2 x + 2 d x

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

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

Add a constant to the solution

= x 2 x + 2 - \frac{1}{3} (2 x + 2)^{\frac{3}{2}} + C

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What is the integral of x/(sqrt(2x+2)) ?
The integral of x/(sqrt(2x+2)) is xsqrt(2x+2)-1/3 (2x+2)^{3/2}+C