How to integrate the following equation?

sine^-x + e^xcose^-x thanks

Question

How to integrate the following equation? 

sine^-x + e^xcose^-x   thanks

hartnn · Answer

u know the property of integral:
$\large \int e^x(f(x)+f'(x) )dx=e^xf(x)+c$
??

anonymous · Answer

no, i have never learnt that before.. what property is it called?

hartnn · Answer

don't know what its called, but using this can u try to solve your integral ?

hartnn · Answer

factor out e^x, then put cos(e^(-x)) = f(x)

zepdrix · Answer

Hmm yah that works nicely :D I'd really like to know what property that is though.. i can't even find it on google...

anonymous · Answer

yupp i can do that with the formula you have given me.. gotten the correct answer, but does anyone here knows the property? really want to take a look. (:

hartnn · Answer

there is no name for this,
just verify it,by differentiating right side

anonymous · Answer

It looks like a specific case of integration of parts,

$$u(x)v(x) = \int\limits_{}^{}u'vdx  + \int\limits_{}^{}uv'dx  $$

but if you select $$u = e^{x}, v = f(x)$$
you get that property

hartnn · Answer

yes, thats ^^ the derivation

anonymous · Answer

THANKS SO MUCH! solved (:

hartnn · Answer

welcome ^_^