What is the integral of (15)/(sqrt(4+5x)) ?

The integral of (15)/(sqrt(4+5x)) is 6sqrt(4+5x)+C

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integral of (15)/(sqrt(4+5x))

\int \frac{15}{4 + 5 x} d x

6 4 + 5 x + C

Solution steps

\int \frac{15}{4 + 5 x} d x

Take the constant out:

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

= 15 \cdot \int \frac{1}{4 + 5 x} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= 15 \cdot \int \frac{1}{5 u} d u

Take the constant out:

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

= 15 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= 15 \cdot \frac{1}{5} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 4 + 5 x

= 15 \cdot \frac{1}{5} \cdot 2 (4 + 5 x)^{\frac{1}{2}}

Simplify

15 \cdot \frac{1}{5} \cdot 2 (4 + 5 x)^{\frac{1}{2}} : 6 4 + 5 x

= 6 4 + 5 x

Add a constant to the solution

= 6 4 + 5 x + C

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What is the integral of (15)/(sqrt(4+5x)) ?
The integral of (15)/(sqrt(4+5x)) is 6sqrt(4+5x)+C