What is the integral of 5/(sqrt(3-2x)) ?

The integral of 5/(sqrt(3-2x)) is -5sqrt(3-2x)+C

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integral of 5/(sqrt(3-2x))

\int \frac{5}{3 - 2 x} d x

- 5 3 - 2 x + C

Solution steps

\int \frac{5}{3 - 2 x} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{3 - 2 x} d x

Apply u-substitution

: \int - \frac{1}{2 u} d u

= 5 \cdot \int - \frac{1}{2 u} d u

Take the constant out:

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

= 5 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

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

= 5 (- \frac{1}{2} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 3 - 2 x

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

Simplify

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

= - 5 3 - 2 x

Add a constant to the solution

= - 5 3 - 2 x + C

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