integrate the?

Question

integrate (4t^2+4)^1/2

can anyone write the last answer of this question (4t^2+4)^1/2= what?

Answer 1

I=[4(t^2+1)^1/2]
now integrate (t^2+1)^1/2 by parts

Answer 2

Optionally, use the substitution t=tan(theta) and get the same answer. Once the 4 factors out, tan^2(theta)+1=1/cos^2(theta) but then you have to do trig integrals, which many people struggle with. Then substitue sin(theta)=t/sqrt(t^2+1) and cos(theta)=1/sqrt(t^2+1) and get (certainly) the same algebraic answer as parts twice (other answer), except maybe for a constant difference. Your textbook should have a similar problem in it.

Answer 3

use u=(4t^2+4) and du = 8tso then use integration by parts twice and u will get
ln(sqrt(t^2+1)+t)+t*sqrt(t^2+1) where is factored the 4 out