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

The integral of (-5)/(sqrt(3w-5)) is -10/3 sqrt(3w-5)+C

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integral of (-5)/(sqrt(3w-5))

\int \frac{- 5}{3 w - 5} d w

- \frac{10}{3} 3 w - 5 + C

Solution steps

\int \frac{- 5}{3 w - 5} d w

Take the constant out:

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

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

Apply u-substitution

: \int \frac{1}{3 u} d u

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

Take the constant out:

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

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

Apply the Power Rule

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

= - 5 \cdot \frac{1}{3} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 3 w - 5

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

Simplify

- 5 \cdot \frac{1}{3} \cdot 2 (3 w - 5)^{\frac{1}{2}} : - \frac{10}{3} 3 w - 5

= - \frac{10}{3} 3 w - 5

Add a constant to the solution

= - \frac{10}{3} 3 w - 5 + C

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What is the integral of (-5)/(sqrt(3w-5)) ?
The integral of (-5)/(sqrt(3w-5)) is -10/3 sqrt(3w-5)+C