What is the integral of 2sqrt(x+1)-2 ?

The integral of 2sqrt(x+1)-2 is 4/3 (x+1)^{3/2}-2x+C

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integral of 2sqrt(x+1)-2

\int 2 x + 1 - 2 d x

\frac{4}{3} (x + 1)^{\frac{3}{2}} - 2 x + C

Solution steps

\int 2 x + 1 - 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x + 1 d x - \int 2 d x

\int 2 x + 1 d x = \frac{4}{3} (x + 1)^{\frac{3}{2}}

\int 2 d x = 2 x

= \frac{4}{3} (x + 1)^{\frac{3}{2}} - 2 x

Add a constant to the solution

= \frac{4}{3} (x + 1)^{\frac{3}{2}} - 2 x + C

\int \frac{x}{x - 11} d x

x^{3} + y^{3} = 3 x y^{2} \frac{d y}{d x}

\int e^{3 x} sin (x) d x

x^{4} - 8 x^{3} + 7 x^{2} - 4, at x = 1

f (x) = 7 e^{e}

What is the integral of 2sqrt(x+1)-2 ?
The integral of 2sqrt(x+1)-2 is 4/3 (x+1)^{3/2}-2x+C