Solving Int. with Trig Substitution for Beginners

[stihl29]

Homework Statement

$$\int\frac{\sqrt{1+x}+\sqrt{1-x}} { \sqrt{1+x}-\sqrt{1-x}}{dx}$$

Homework Equations

I believe trig substitution can be used here. I'm not very good at calculus only beginning to take calc classes, and guideance would be wonderful. because i want to get better.

The Attempt at a Solution

I don't have any idea on what to substitute.
x = some thing like x^2 ??
or u = 1 - x
and u = 1 + x ??

 

[Dick]

The first thing you want to do is simplify the expression algebraically. It will help to rationalize the denominator by multiplying numerator and denominator by sqrt(1-x)+sqrt(1+x). The trick here is that (sqrt(a)-sqrt(b))*(sqrt(a)+sqrt(b))=a-b. Try simplifying it and see how far you can get.

 

[stihl29]

ohhhh, thank you, i can't attempt it at this moment but your solution looks promising !