What is the integral of (30)/(sqrt(2x+4)) ?

The integral of (30)/(sqrt(2x+4)) is 30sqrt(2x+4)+C

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integral of (30)/(sqrt(2x+4))

\int \frac{30}{2 x + 4} d x

30 2 x + 4 + C

Solution steps

\int \frac{30}{2 x + 4} d x

Take the constant out:

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

= 30 \cdot \int \frac{1}{2 x + 4} d x

Apply u-substitution

= 30 \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

= 30 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

= 30 \cdot \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 2 x + 4

= 30 \cdot \frac{1}{2} \cdot 2 (2 x + 4)^{\frac{1}{2}}

Simplify

30 \cdot \frac{1}{2} \cdot 2 (2 x + 4)^{\frac{1}{2}} : 30 2 x + 4

= 30 2 x + 4

Add a constant to the solution

= 30 2 x + 4 + C

What is the integral of (30)/(sqrt(2x+4)) ?
The integral of (30)/(sqrt(2x+4)) is 30sqrt(2x+4)+C