What is the integral of 5/(sqrt(x+6)) ?

The integral of 5/(sqrt(x+6)) is 10sqrt(x+6)+C

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integral of 5/(sqrt(x+6))

\int \frac{5}{x + 6} d x

10 x + 6 + C

Solution steps

\int \frac{5}{x + 6} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{x + 6} d x

Apply u-substitution

: \int 2 d u

= 5 \cdot \int 2 d u

Integral of a constant:

\int a d x = a x

= 5 \cdot 2 u

Substitute back

u = x + 6

= 5 \cdot 2 x + 6

Simplify

= 10 x + 6

Add a constant to the solution

= 10 x + 6 + C

y = x - 4, y^{2} = 2 x

x \to + 0 lim (x ln (\frac{1}{x}))

(sin (x)) (sec (x))

\int_{- 1}^{1} \frac{1}{2} (1 - x^{4}) d x

\int \frac{x ^{3} + 5 x + 1}{x ^{2} + 5} d x

What is the integral of 5/(sqrt(x+6)) ?
The integral of 5/(sqrt(x+6)) is 10sqrt(x+6)+C