# Homework Help: Integration of a complicated radical function

1. Dec 4, 2013

### kashan123999

1. The problem statement, all variables and given/known data

∫(√x).[√(x+1)] dx

2. Relevant equations

3. The attempt at a solution

Sorry but i couldn't get it any far than this u substitution

u = √(x+1)
du = [(1)/{2√(x+1)}]dx

→ dx = [2√(x+1)]du

putting in the main expression

∫ √(u2 - 1). 2u2 du

2. Dec 4, 2013

### Staff: Mentor

Here's a different approach. Combine the two radicals like so:
$\int \sqrt{x}\sqrt{x + 1}dx = \int \sqrt{x^2 + x}dx$

Now, complete the square inside the radical to get √[(x + a)2 - b2]. At this point a trig substitution should work, assuming you have learned that technique.

3. Dec 4, 2013

### kashan123999

so that was mathematically valid : O to multiply..poor algebra me :(