The Attempt at a Solution
Well I started off first by taking t=sqrt(x) but that didn't get me very far. So then I decided to make x equal to t^2 which sort of worked. After hours of struggle I decided to have a look at the answers and I was pretty close but I am stumped by some steps in the answers.
Here's an image
First off I don't quite get how you are allowed to put t^2 in the differential.. no one ever taught me that. Then I don't understand how all of a sudden the first circled thing came about.
Does dt^2 mean that it's the second derivative? Did they take the integral in the second step (the circled part)? What happened there... Suddenly the square gets put on the t in the integrand and a 2 gets put outside of the integral.. whut?!
A friend of mine told me that dt^2 = dt*dt and then he blabbered on and got some weird solution...
Then the second circle. How the heck did they get the 2 there? It looks to me that they used t^2 as u and e^t as dv.
This is really mind blowing... because of this problem, everything I have learned in calculus seams useless because none of the rules make sense now to me... :(
Please help! :)
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