Substitution Rule Integral Questions
I have a few questions I'm unsure about, the first one is a indefinite integral:
1.) Find: antiderivative sqrt(1+lnx)*lnx*1/x dx
I got 2u^(5/2)/5 - 2u^(3/2)/3 for this one where u=1+lnx
The next two are definite
2.) antiderivative 2x/sqrt(4x^2 + 3) dx where the interval is between 0 and 2
For this one, I got 1/4*antiderivative 1/sqrtu where u=4x^2 + 3 and the interval is between 3 and 19. The problem is that when I sub in the x's back in for u and do the math (the interval changes back to 0/2, then I get a completely different answer for both.
3.) antiderivative x/(x^2+1)ln(x^2+1)
For this one, I get an antiderivative of 1/2ln|u| between 0.69 and 1.61 when u = ln(x^2+1). Doing the math, I get 0.42 as the answer.
But when I sub the x's back in, the antiderivative changes to 1/2ln|x^2+1| between 1 and 2 and I get 0.46 for my answer. So either I'm making a mistake or the two aren't equal.