(New page: I have been working out some cases where I can't integrate through trigonometric substitutions (or at least, not easily) but I can using hyperbolic functions. See if you can solve <math>...) |
|||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
I have been working out some cases where I can't integrate through trigonometric substitutions (or at least, not easily) but I can using hyperbolic functions. See if you can solve | I have been working out some cases where I can't integrate through trigonometric substitutions (or at least, not easily) but I can using hyperbolic functions. See if you can solve | ||
| − | <math>\int x^2\sqrt{x^2+1}</math> | + | <math>\int x^2\sqrt{x^2+1}dx</math> |
Special points if you can solve it using trig functions. | Special points if you can solve it using trig functions. | ||
| Line 10: | Line 10: | ||
--[[User:Jmason|John Mason]] | --[[User:Jmason|John Mason]] | ||
| + | |||
| + | Why couldn't you substitute x^2+1 for u and say x^2 = u-1. then, distribute and just use the power rule. There is no need for trig substitution for this. - G Briz | ||
| + | |||
| + | That works wonder if the first part of the integral is x to the third power, but in this case, you end up with an uneliminatable x in the derivative of u. -- [[User:Jmason|John Mason]] | ||
Latest revision as of 11:37, 1 November 2008
I have been working out some cases where I can't integrate through trigonometric substitutions (or at least, not easily) but I can using hyperbolic functions. See if you can solve
$ \int x^2\sqrt{x^2+1}dx $
Special points if you can solve it using trig functions.
The method and thought process
Why couldn't you substitute x^2+1 for u and say x^2 = u-1. then, distribute and just use the power rule. There is no need for trig substitution for this. - G Briz
That works wonder if the first part of the integral is x to the third power, but in this case, you end up with an uneliminatable x in the derivative of u. -- John Mason
