(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The definite integral of (t^3 + t -1)/(sin(t)) from 2 to x^2

2. Relevant equations

3. The attempt at a solution

First off, I don't have the solution anywhere, my teacher just gave this to us to work on for the final exam review.

I can think of a few things. I know for the definite integrals you can first simplify the expression as an indefinite integral, then use the fundamental theorem to solve. I know the integral of 1/sin(t)=ln(sint), and integral of (t^3 + t -1)=(t^4/4 + t^2/2 -t) so for the indefinite integral I have..

(t^4/4 + t^2/2 -t)ln(sint). do I then just plug in the upper and lower limits to simplify? I kind of feel like I'm on the wrong track because it looks sloppy and usually he gives us problems that have reasonable looking solutions.

Another attempt is that I recognized 1/sin(t)=csc(t). So then I am left with the integral of (t^3 + t -1)(csc(t))... but I'm not sure if substitution would work.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Definite integral of rational function

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