Wolfram Alpha says that the answer is , but it does not show steps (unfortunately).(Headbang)

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- Jan 13th 2012, 04:09 AMAgentSmithintegral

Wolfram Alpha says that the answer is , but it does not show steps (unfortunately).(Headbang) - Jan 13th 2012, 04:10 AMProve ItRe: integral
- Jan 13th 2012, 04:14 AMbugatti79Re: integral
- Jan 13th 2012, 05:07 AMsbhatnagarRe: integral
Euler said " "

We have

Subtract [2] from [1]

Substitute and .

- Jan 13th 2012, 05:48 AMAgentSmithRe: integral
- Jan 13th 2012, 08:43 AMOpalgRe: integral
Once you have seen the Wolfram Alpha solution, you can reconstruct it like this. Start with the addition formula then

Therefore

(But I think you would be unlikely to find that method if you had not already seen the answer.) - Jan 13th 2012, 08:52 AMRidleyRe: integral
How does Wolfram Alpha (Mathematica) even solve integrals like this one?

- Jan 13th 2012, 10:28 PMsbhatnagarRe: integral
Mathematica's Integrate function represents the fruits of a huge amount of mathematical and computational research. It doesn't do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match up undetermined symbolic parameters. Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica's strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions.