What is the integral of sqrt(9x+5) ?

The integral of sqrt(9x+5) is 2/27 (9x+5)^{3/2}+C

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integral of sqrt(9x+5)

\int 9 x + 5 d x

\frac{2}{27} (9 x + 5)^{\frac{3}{2}} + C

Solution steps

\int 9 x + 5 d x

Apply u-substitution

: \int \frac{u}{9} d u

= \int \frac{u}{9} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{9} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{9} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 9 x + 5

= \frac{1}{9} \cdot \frac{2}{3} (9 x + 5)^{\frac{3}{2}}

Simplify

\frac{1}{9} \cdot \frac{2}{3} (9 x + 5)^{\frac{3}{2}} : \frac{2}{27} (9 x + 5)^{\frac{3}{2}}

= \frac{2}{27} (9 x + 5)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{27} (9 x + 5)^{\frac{3}{2}} + C

x \to - 6 + lim (\frac{- 2 x}{x + 6})

(0.2) (2)

\frac{d}{d x} (x^{10} e^{x + 1})

\frac{d y}{d t} = y (1 - y), y (0) = 16

\int \frac{t ^{2} - 1}{t ^{4} - 1} d t

What is the integral of sqrt(9x+5) ?
The integral of sqrt(9x+5) is 2/27 (9x+5)^{3/2}+C