What is the integral of sqrt(9/(5-6x)) ?

The integral of sqrt(9/(5-6x)) is -sqrt(5-6x)+C

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integral of sqrt(9/(5-6x))

\int \frac{9}{5 - 6 x} d x

- 5 - 6 x + C

Solution steps

\int \frac{9}{5 - 6 x} d x

Simplify

\frac{9}{5 - 6 x} : \frac{3}{5 - 6 x}

= \int \frac{3}{5 - 6 x} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{5 - 6 x} d x

Apply u-substitution

: \int - \frac{1}{6 u} d u

= 3 \cdot \int - \frac{1}{6 u} d u

Take the constant out:

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

= 3 (- \frac{1}{6} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 3 (- \frac{1}{6} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 5 - 6 x

= 3 (- \frac{1}{6} \cdot 2 (5 - 6 x)^{\frac{1}{2}})

Simplify

3 (- \frac{1}{6} \cdot 2 (5 - 6 x)^{\frac{1}{2}}) : - 5 - 6 x

= - 5 - 6 x

Add a constant to the solution

= - 5 - 6 x + C

\frac{( 2 s + 1 )}{s ^{2} + 5 s + 6}

\frac{d y}{d t} = \frac{9}{40} - \frac{y}{200}

f (xg (x))

x^{\frac{11}{2}}, 5

\frac{d}{d x} (5 x^{2} e^{3 x - 7})

What is the integral of sqrt(9/(5-6x)) ?
The integral of sqrt(9/(5-6x)) is -sqrt(5-6x)+C