Hello, I was hoping someone could pick off where I went wrong on these two questions. As far as I can tell I have the right answers but the program I am plugging the answers into says nay. Not sure on how to do the integral symbol on this forum so just assume it is there.
1) Integrate by partial fractions
Using the partial fractions I was able to change it to which is so far correct according to the program (in bx+c on the top of the second fraction the c is 0)
So I am down to integrating and . Using the natural log rule the first I figure is 2ln(x+1) and the second I solved using and getting 1/2du=x. The 1/2 comming outside of the integral it leaves 1/2 the integral of du/u, which is 1/2ln(u), which then gives you -4(1/2)ln(x^2+4) as the second integral.
So I figured should be the answer, but it comes back as wrong and I am running out of attempts with no clue where I am wrong on this.
Integral of A hint is given to use u=e^x which I did getting -33u-126/u^2+9u+18, factoring the bottom leaves (u+3) and (u+6) for the partial fractions. I got -9/(u+3) and -24/(u+6) for the two partial fractions to solve. I ended up with -9ln(e^x+3)-24ln(e^x+6) when intrgrating and putting back in e^x for u, which is wrong.
Can anyone help me with where I am going wrong on either or both of these questions? I am guessing it might be the same problem on each, missing something I am supposed to do.
Ack! I wrote that down a tiny bit wrong, it is actually -4x/(X^2+4), given that -4 was b but the x is still in the bx+c which changes stuff abit. I ran it through Wolframs integrator and it gives me the same -2ln(x^2+4) answer that I got the long way that comes up as wrong. I got the answer for the second question finally though, your catching that e^x thing helped huge.
Thanks for the help Mr. F