Solving Integral of (4/(x^2+4))2 using Trig Substitution

[mattmannmf]

find the integral:

integral (4/(x^2+4))2

Ill use S for my integral
So what i did so far is move the 4^2 out of the integral and get this:

16 S 1/(x^2+4)^2

I tried using partial fractions but got nothing. I am not sure what to do. So far all I have learned was U sub, integral by parts, partial fractions, and trig substitution.

Would trig substitution work?
if i make x=2tan (theta)

or is there another method i haven't seen yet.

 

[rock.freak667]

Yes that substitution will work well. Try it and remember your trig identities.

 

[mattmannmf]

the answer i got when i did it was:

.5archtan(x/2) +x(x^2+4) + C

is that what you guys got?
i made x=2tan (theta)
dx= 2sec^2(theta)

 

[rock.freak667]

the answer i got when i did it was:

.5archtan(x/2) +x(x^2+4) + C

is that what you guys got?
i made x=2tan (theta)
dx= 2sec^2(theta)

Your first term is correct, where did you get the x(x²+4) term from?

 

[mattmannmf]

that came from the 2nd half of the equation
i had the integral:
S cos^2 theta
used the power reducing formulas
S (1+cos2 theta)/2
and took derivative (just talking about
= .5 d(theta) + S .5 cos2theta
took derivative and used the double angle formula for the cos 2 theta (its would be .5 sin 2 theta when derivative taken)

and answer came out to be:
.5 arctan (x/2) + .25* 2 sin (theta) cos (theta)

sin theta= x... oh wait i did x*sqr x^2 + 4... not divided
THANKS!
im going to redue my work and show my final answer.