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 |
Euler's substitution writes the radicand's powers in its variable as powers of the root:
Q^(k/2)as the root to thekth, which is right, and a whole powerQ^nas the root to thenth, which isQ^(n/2). The integrand it went on to integrate was not the one asked:18038b0d1/((x^2 + 3)^2 (x + sqrt(x^2 + 3)))(x^2 + 3)^2/(x + sqrt(x^2 + 3))[0.2, 1.7]its answer changes by2.08, where the integral is8.48(x^2 + 3)^3/(1 + sqrt(x^2 + 3))