Learning Complicated Integrals from a Simple Integral in mathHandbook.com

Learning Complicated Integrals from a Simple Integral 
              
just define one integral of f(x) is f(x) - x, it will know not only the integral of f(x), but also f(x+1), 2*f(2*x+2), etc. 
  
IN:  integrate(f(x_), x_) := f(x) - x; integrate(2*f(x+1)) 
OUT: 2*f(x+1) - 2*(x+1) 


reference math handbook 
www.mathHandbook.com 

On 07.06.2017 8:18, drhuang57@gmail.com wrote:
> Learning Complicated Integrals from a Simple Integral
>
> just define one integral of f(x) is f(x) - x, it will know not only the integral of f(x), but also f(x+1), 2*f(2*x+2), etc.
>
> IN:  integrate(f(x_), x_) := f(x) - x; integrate(2*f(x+1))
> OUT: 2*f(x+1) - 2*(x+1)
>
>
> reference math handbook
> www.mathHandbook.com
>

What's complicated in a simple change of variables?

Gene

On Wednesday, 7 June 2017 20:15:12 UTC+10, Evgeny Filatov  wrote:
> On 07.06.2017 8:18, drhuang57@gmail.com wrote:
> > Learning Complicated Integrals from a Simple Integral
> >
> > just define one integral of f(x) is f(x) - x, it will know not only the integral of f(x), but also f(x+1), 2*f(2*x+2), etc.
> >
> > IN:  integrate(f(x_), x_) := f(x) - x; integrate(2*f(x+1))
> > OUT: 2*f(x+1) - 2*(x+1)
> >
> >
> > reference math handbook
> > www.mathHandbook.com
> >
> 
> What's complicated in a simple change of variables?
> 
> Gene

It learns the complicated integrals, e.g. 2f(2x+1), from a single simple integral of f(x).

> > reference math handbook
> > www.mathHandbook.com

On Wed, 07 Jun 2017 20:52:50 -0700, drhuang57 wrote:

> On Wednesday, 7 June 2017 20:15:12 UTC+10, Evgeny Filatov  wrote:
>> On 07.06.2017 8:18, drhuang57@gmail.com wrote:
>> > Learning Complicated Integrals from a Simple Integral
>> >
>> > just define one integral of f(x) is f(x) - x, it will know not only
>> > the integral of f(x), but also f(x+1), 2*f(2*x+2), etc.
>> >
>> > IN:  integrate(f(x_), x_) := f(x) - x; integrate(2*f(x+1))
>> > OUT: 2*f(x+1) - 2*(x+1)
>> >
>> >
>> > reference math handbook www.mathHandbook.com
>> >
>> >
>> What's complicated in a simple change of variables?
>> 
>> Gene
> 
> It learns the complicated integrals, e.g. 2f(2x+1), from a single simple
> integral of f(x).

Oooh f***ing ahhh.  That's hardly a complicated integral.

-- 

Tim Wescott
Wescott Design Services
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