# Trig substitution

## Homework Statement

Did I make a mistake here somewhere? The solution in the back of the book is completely different. Seems like they used trig sub one step later or something. I can't find any error in my logic. Test coming up soon and I'm confused and panicking -_-!
Actually I just found a mistake with my constants! But apart from that, is it correct? The first term should be multiplied with -1/2 and the second with 3/2.

## The Attempt at a Solution

Dick
Homework Helper
I doubt it's right, but it's too hard to read to make sure. I'd really suggest you write (x+4)=(x+1)+3 at the beginning and use that to split the integral into two much more manageable parts.

I don't see how that makes it more manageable. That was my original plan but the numerator isn't my problem. No matter what I do I'm stuck with this denominator that's ugly.

Dick
Homework Helper
I don't see how that makes it more manageable. That was my original plan but the numerator isn't my problem. No matter what I do I'm stuck with this denominator that's ugly.

The numerator is your problem. (x+1)/((x+1)^2+4) is an easy substitution. 3/((x+1)^2+4) is an easy arctan problem after the correct substitution. Divide and conquer. Don't try to do it all in one lump.

ehild
Homework Helper
simplify the cos(arctan((x+1)/2)) term.

ehild

1 person
Dick
Homework Helper
simplify the cos(arctan((x+1)/2)) term.

ehild

My point was not that you can't salvage that attempt by correcting a few errors, but that there is an easier strategy to do it to begin with.

ehild
Homework Helper
My point was not that you can't salvage that attempt by correcting a few errors, but that there is an easier strategy to do it to begin with.

For me, the solution looks good (when correcting the constants) but the OP can bring it to a simpler form. He is familiar with the trigonometric substitution, and he will do it anyway when integrating 1/((x+1)2+4). You discourage the OP suggesting to discard his method.

ehild

Dick