This antiderivative has arguable the highest ratio of “really hard to compute” to “really easy to write”:

So far, I’ve shown that the denominator can be factored over the real numbers:

To evaluate the remaining two integrals, I’ll use the antiderivative

.

To begin, I’ll complete the squares:

Applying the substitutions and , I can continue:

Combining, I finally arrive at the answer for :

Naturally, this can be checked by differentiation, but I’m not going type that out.

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*Posted by John Quintanilla on October 6, 2015*

https://meangreenmath.com/2015/10/06/the-antiderivative-of-1x41-part-6/

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