Find ∫(x^2+x+5)/√(x^2+1)dx using a table of integrals
These are the forms I chose to use:
#1 ∫(u^2)/(√(u^2 + a^2))du = (u/2)*(√(a^2 + u^2)) - (a^2/2)(ln(u+√(a^2 + u^2) + C
#3 ∫(du)/(√(a^2 + u^2)) = ln(u + √(a^2 + u^2) +C
The Attempt at a Solution
I won't show every step, but here's what I did:
1. Split the single integral up into three separate integrals.
2. For the first, I let u=x and a=1. I then plugged into the formula and got...
(x/2)*√(1+x^2)-(1/2)*ln(x+√(1+x^2)) + C
3. Solve the second with just a u substitution...
= √(x^2 + 1) + C
4. Solve the third with a table... I got
= 3*√(1+x^2) + 9*ln(x+ √(1+x^2))/2 + C
I'm pretty sure that I used the correct integrations from the table, and I can't seem to see where I went wrong. I know the final answer just by using Maple. I think I can also solve it without using a table. I would use trig to do that, but that's not what this homework is testing us on.
I sincerely apologize for my lack of LaTex use...
If you want to know more of the steps I took, just say so and I will post a picture of my work.