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

The integral of (5+5sqrt(x+5))/(sqrt(x+5)) is 10sqrt(x+5)+5x+C

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

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

10 x + 5 + 5 x + C

Solution steps

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

Expand

\frac{5 + 5 x + 5}{x + 5} : \frac{5}{x + 5} + 5

= \int \frac{5}{x + 5} + 5 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{5}{x + 5} d x + \int 5 d x

\int \frac{5}{x + 5} d x = 10 x + 5

\int 5 d x = 5 x

= 10 x + 5 + 5 x

Add a constant to the solution

= 10 x + 5 + 5 x + C

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What is the integral of (5+5sqrt(x+5))/(sqrt(x+5)) ?
The integral of (5+5sqrt(x+5))/(sqrt(x+5)) is 10sqrt(x+5)+5x+C