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

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

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

\int \frac{1}{1 + u} d u

2 1 + u + C

Solution steps

\int \frac{1}{1 + u} d u

Apply u-substitution

: \int 2 d v

= \int 2 d v

Integral of a constant:

\int a d x = a x

= 2 v

Substitute back

v = 1 + u

= 2 1 + u

Add a constant to the solution

= 2 1 + u + C

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