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

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

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

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

300 2 x + 25 + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 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

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

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

Substitute back

u = 2 x + 25

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

Simplify

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

= 300 2 x + 25

Add a constant to the solution

= 300 2 x + 25 + C

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x \to - 2 lim (2 x^{3} - x^{2} + 7 x - 3)

(2.6) (- 2.6)

x \to 2 lim (\frac{\frac{2}{x} - 1}{2 - x})

\int \frac{x ^{2} - 2 x - 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

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