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Euler's substitution reads a whole power of the radicand as half of it #1770
Description
Euler's substitution writes the radicand's powers in its variable as powers of the root: Q^(k/2) as the root to the kth, which is right, and a whole power Q^n as the root to the nth, which is Q^(n/2). The integrand it went on to integrate was not the one asked:
| integrand | 2.5.0 | master 18038b0d |
|---|---|---|
1/((x^2 + 3)^2 (x + sqrt(x^2 + 3))) |
declined | wrong at every real point |
(x^2 + 3)^2/(x + sqrt(x^2 + 3)) |
declined | wrong: over [0.2, 1.7] its answer changes by 2.08, where the integral is 8.48 |
(x^2 + 3)^3/(1 + sqrt(x^2 + 3)) |
declined | wrong at every real point |
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