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

The integral of (x+3)^{3/2} is 2/5 (x+3)^{5/2}+C

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integral of (x+3)^{3/2}

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

\frac{2}{5} (x + 3)^{\frac{5}{2}} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: \frac{2}{5} u^{\frac{5}{2}}

= \frac{2}{5} u^{\frac{5}{2}}

Substitute back

u = x + 3

= \frac{2}{5} (x + 3)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{5} (x + 3)^{\frac{5}{2}} + C

(- 4, 1), (1, - 2)

f (x) = x^{3} + 4 x^{2} + 4 x, at x = - 1

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

\int (3 x^{2} - 1) e^{x} d x

\int csc (\frac{a x}{b}) cot (\frac{a x}{b}) d x

What is the integral of (x+3)^{3/2} ?
The integral of (x+3)^{3/2} is 2/5 (x+3)^{5/2}+C