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

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

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

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

2 1 + y + x + C

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

= 2 u^{\frac{1}{2}}

Substitute back

u = 1 + y + x

= 2 (1 + y + x)^{\frac{1}{2}}

Apply radical rule:

= 2 1 + y + x

Add a constant to the solution

= 2 1 + y + x + C

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