What is the integral of 3/(sqrt(x+9)) ?

The integral of 3/(sqrt(x+9)) is 6sqrt(x+9)+C

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integral of 3/(sqrt(x+9))

\int \frac{3}{x + 9} d x

6 x + 9 + C

Solution steps

\int \frac{3}{x + 9} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{x + 9} d x

Apply u-substitution

: \int 2 d u

= 3 \cdot \int 2 d u

Integral of a constant:

\int a d x = a x

= 3 \cdot 2 u

Substitute back

u = x + 9

= 3 \cdot 2 x + 9

Simplify

= 6 x + 9

Add a constant to the solution

= 6 x + 9 + C

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What is the integral of 3/(sqrt(x+9)) ?
The integral of 3/(sqrt(x+9)) is 6sqrt(x+9)+C