__Category__: Integral Calculus, Algebra"Published in Suisun City, California, USA"

Evaluate

__Solution__:

Consider the given equation above

In this type of equation, we cannot integrate it by a simple integration because both the numerator and the denominator have radical equations. If you will rationalize the denominator in order to eliminate the radical sign, then the numerator still has radical equations and the above equation will be more complicated. To eliminate the radical signs at the numerator and the denominator, we have to use the Algebraic Substitution as follows

If

then

Substitute the values of √x , √x + 1, and dx to the above equation, we have

but

Hence, the above equation becomes

Therefore, the final answer is