Integral With Constant Numerator
by Braden
(Botswana)
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:
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