Thread: Indefinite Integral Help - Greatly Appreciated!

I have some problems for indefinite integrals, which I need some assistance with, a detailed explanation of the steps taken to solve would be the most helpful, as the answers are provided. This is my first post on this forum, and would really really appreciate any help anyone can offer. Thanks!

The problems I'm having trouble solving are:
∫(2x-3)/(x^2-3x+8) dx

∫x/(x^2+1) dx

∫(x)√(x^2+3) dx

∫sin^2 x dx

∫tan^4 x dx

Thanks a lot!

Originally Posted by Robbie

I have some problems for indefinite integrals, which I need some assistance with, a detailed explanation of the steps taken to solve would be the most helpful, as the answers are provided. This is my first post on this forum, and would really really appreciate any help anyone can offer. Thanks!

The problems I'm having trouble solving are:
∫(2x-3)/(x^2-3x+8) dx

antiderivative is an ln ... see the form u'/u ?

∫x/(x^2+1) dx

ln for this one, too ... just need a constant

∫(x)√(x^2+3) dx

use a substitution ... let u = x^2 + 3

∫sin^2 x dx

power reduction identity ... sin^2 x = [1 - cos(2x)]/2

∫tan^4 x dx

use another identity ... tan^2 x + 1 = sec^2 x ...

tan^4 x = tan^2 x(sec^2 x - 1) = tan^2 x sec^2 x - tan^2 x =
tan^2 x sec^2 x - (sec^2 x - 1)

Thanks a lot!