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

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

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

\int (\frac{1}{x + 1}) d x

2 x + 1 + C

Solution steps

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

= 2 x + 1

Add a constant to the solution

= 2 x + 1 + C

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