Evaluate integral by using integration by parts: intcos^-1x dx?
intcos^-1x dx
I'm stuck on one particular part, here's what I've got so far:
u=cos^-1x
du=-1/sqrt(1-x^2)dx
v=x
dv=dx
intudv=uv-intvdu
=xcos^-1x-int-x/sqrt(1-x^2)dx
t=1-x^2
dt=-2xdx
=xcos^-1x-int-x/sqrtt(dt/(-2x))
=xcos^-1x-intdt/(2sqrtt)
after that I don't know what to do
I'm stuck on one particular part, here's what I've got so far:
after that I don't know what to do
1 Answer
See below
Explanation:
For this bit that follows, I'd argue that the sub is a OTT and that, if you know the derivative of
But moving forward with the sub:
Set up for power rule if that helps visualise:
Apply power rule
Reversing out of the sub:
Overall, keep an eye on that minus sign :)