What is the integral of (300)/(sqrt(2q+25)) ?

The integral of (300)/(sqrt(2q+25)) is 300sqrt(2q+25)+C

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integral of (300)/(sqrt(2q+25))

\int \frac{300}{2 q + 25} d q

300 2 q + 25 + C

Solution steps

\int \frac{300}{2 q + 25} d q

Take the constant out:

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

= 300 \cdot \int \frac{1}{2 q + 25} d q

Apply u-substitution

= 300 \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

= 300 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

= 300 \cdot \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 2 q + 25

= 300 \cdot \frac{1}{2} \cdot 2 (2 q + 25)^{\frac{1}{2}}

Simplify

300 \cdot \frac{1}{2} \cdot 2 (2 q + 25)^{\frac{1}{2}} : 300 2 q + 25

= 300 2 q + 25

Add a constant to the solution

= 300 2 q + 25 + C

What is the integral of (300)/(sqrt(2q+25)) ?
The integral of (300)/(sqrt(2q+25)) is 300sqrt(2q+25)+C