integration by parts help (1 Viewer)

[boredguy]

how do i know which one to make U and which one do make dV?
is there a rule i can use to distinguish which one i should be using?
eg. if i have sinxlnx or sin^-1xe^x which one shud i use for u and for dv

 

[Riviet]

Usually, you let u be the one that's harder to integrate. You can use LIATE, which stands for logarithm-inverse trig-algebraic-trig-exponential to decide which to let u equal. Using LIATE, log would take priority and exponential would have least priority.
So for sinx.lnx, you would let u=lnx and for sin^-1x you would let u=sin^-1x.

 

[_ShiFTy_]

As Riviet said, you can use LIATE...but its really just common sense. e.g. if you have sinxlnx, you know you cant integrate lnx, so you let u = lnx

When it comes to reduction involving by parts, always look at what the answer looks like. If it has n+1, you know you have to integrate something that will give you an n+1.