Integral With Constant Numerator

by Braden

How do I integrate such integrals with constant numerator and denominator without square root?

Answer by Pablo:

This integral does not have a square root but falls into the third case of trigonometric substitution. Look it up here: Trigonometric Substitution.

Using the substitution of the third case we make:

Making these substitutions and using the trigonometric identity for the third case:

Now we only need to solve this trigonometric integral and make the inverse substitutions. This trigonometric integral is solved as an example in this page: Trigonometric Integrals. The result is:

Now, substituting back:

And now using the following trigonometric identities:

We have the answer is:

Return to Trigonometric Substitution

Comments for Integral With Constant Numerator

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Aug 09, 2013
Integration with constants
by: TestAbhyas

Wonderfully explained. Worth sharing in coaching classes.

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