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

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

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integral of (x+3)sqrt(x+3)

\int (x + 3) x + 3 d x

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

Solution steps

\int (x + 3) x + 3 d x

Simplify

(x + 3) x + 3 : (x + 3)^{\frac{3}{2}}

= \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

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 1

\frac{\partial}{\partial r} (r cos (s))

y = x, y = \frac{1}{2} x, x = 16

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

y = 5 - x

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