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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
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
