What is the integral of sqrt(x+9) ?

The integral of sqrt(x+9) is 2/3 (x+9)^{3/2}+C

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integral of sqrt(x+9)

\int x + 9 d x

\frac{2}{3} (x + 9)^{\frac{3}{2}} + C

Solution steps

\int x + 9 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 + 9

= \frac{2}{3} (x + 9)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x + 9)^{\frac{3}{2}} + C

\int_{- 2}^{1} (x - 4 ∣ x ∣) d x

y^{^{''}} - 4 y = e^{- 2 x} - 2 x

\int cos (10 x) cos (3 x) d x

f (x) = x + \frac{2}{x}, at x = 3

What is the integral of sqrt(x+9) ?
The integral of sqrt(x+9) is 2/3 (x+9)^{3/2}+C