What is the integral of 1/(sqrt(x+2)) ?

The integral of 1/(sqrt(x+2)) is 2sqrt(x+2)+C

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integral of 1/(sqrt(x+2))

\int \frac{1}{x + 2} d x

2 x + 2 + C

Solution steps

\int \frac{1}{x + 2} d x

Apply u-substitution

= \int 2 d u

Integral of a constant:

\int a d x = a x

= 2 u

Substitute back

u = x + 2

= 2 x + 2

Add a constant to the solution

= 2 x + 2 + C

What is the integral of 1/(sqrt(x+2)) ?
The integral of 1/(sqrt(x+2)) is 2sqrt(x+2)+C