Some husbands try to impress their wives by lifting extremely heavy objects or other extraordinary feats of physical prowess.

That will never happen in the Quintanilla household in a million years.

But she was impressed that I broke an impasse in her research and resolved a discrepancy between Mathematica 4 and Mathematica 8 by finding the following integral by hand in less than an hour:

Yes, I married well indeed.

In this post, I collect the posts that I wrote last summer regarding various ways of computing this integral.

Part 2a,

2b,

2c,

2d,

2e,

2f: Changing the endpoints of integration, multiplying top and bottom by

, and the substitution

.

Part 3a,

3b,

3c,

3d,

3e,

3f,

3g,

3h,

3i: Double-angle trig identity, combination into a single trig function, changing the endpoints of integration, and the magic substitution

.

Part 4a,

4b,

4c,

4d,

4e,

4f,

4g,

4h: Double-angle trig identity, combination into a single trig function, changing the endpoints of integration, and contour integration using the unit circle

Part 5a,

5b,

5c,

5d,

5e,

5f,

5g,

5h,

5i,

5j: Independence of the parameter

, the magic substitution

, and partial fractions.

Part 6a,

6b,

6c,

6d,

6e,

6f,

6g:Independence of the parameter

, the magic substitution

, and contour integration using the real line and an expanding semicircle.

Part 7: Concluding thoughts… and ways that should work that I haven’t completely figured out yet.

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*Related*

*Posted by John Quintanilla on January 6, 2016*

https://meangreenmath.com/2016/01/06/how-i-impressed-my-wife-index/