What is the integral of (x+1)/(sqrt(x+1)) ?

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

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integral of (x+1)/(sqrt(x+1))

\int \frac{x + 1}{x + 1} d x

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

Solution steps

\int \frac{x + 1}{x + 1} d x

Simplify

\frac{x + 1}{x + 1} : x + 1

= \int x + 1 d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = x + 1

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

Add a constant to the solution

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

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x \to 0 lim ((1 + 4 x)^{\frac{4}{x}})

\frac{\partial}{\partial x} \frac{2 t}{( 1 - \frac{0.5 ( x )}{L} ) ^{2}}

\frac{d}{d x} (\frac{1}{csc ( x ) + cot ( x )})

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