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

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

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integral of sqrt(x+3)-3

\int x + 3 - 3 d x

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

Solution steps

\int x + 3 - 3 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 x + 3 d x - \int 3 d x

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

x + y y^{^{'}} = 0

y = x^{3} + 7 x^{2} - 4

\frac{d y}{d t} = 4 t - 0.1 y t

x^{2} - 5 x + 1

- \frac{2 x ^{2}}{5 y ^{2}}

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