In the first integration have you written, Please confirm this and then I will try to help.
Hello guys, just finish learning about Derivatives and Limits yesterday, so I thought I could get started on Integration now.
I've looked in alot of places but can't find out how to integrade a multiplication/division! I mean, addition and subtraction are easy stuff, just distribute the integral sign but how are multiplication, division handled?
Integrate: 3x(Cos(x^3 + 7))
Thanks for any help!
Just in case a picture helps...
... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. And integration by parts is a matter of filling out this rule usefully but starting (unlike in differentiation) with one of the lower corners instead of at the top. So the basic pattern is...
... and choosing legs crossed or uncrossed is equivalent to asigning u, v, and du and dv
By the way, other brands of IBP are available. E.g. tabular. And of course this is 'integration by parts thrice', because we have to repeat the pattern until the order of the polynomial goes to zero.
And I take it this is a new example you're asking about - if you wanted to tackle the 3x(Cos(x^3 + 7)) by parts then, no, no deal. Can't be expressed as elementary means can't be done, basically (roughly).
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!