What is the integral of sqrt(u+1) ?

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

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integral of sqrt(u+1)

\int u + 1 d u

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

Solution steps

\int u + 1 d u

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{2}{3} v^{\frac{3}{2}}

= \frac{2}{3} v^{\frac{3}{2}}

Substitute back

v = u + 1

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

Add a constant to the solution

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

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