- #1
PCSL
- 146
- 0
first off, i can solve this problem easily with u-sub but the question asks to use trig sub.
[itex]\int[/itex]4x/(x2+1)
then i have x=tan(theta)
dx=sec2(theta)
=[itex]\int[/itex]4tan(theta)sec2(theta)/(tan2(theta)+1)
=[itex]\int[/itex]4tan(theta)d(theta)
=-4ln(cos(theta))=-4ln(cos(arctan(x)))
thanks for the help, this problem is driving me crazy since it appears so simple.
edit: The answer is 2ln(x2+1)+C
[itex]\int[/itex]4x/(x2+1)
then i have x=tan(theta)
dx=sec2(theta)
=[itex]\int[/itex]4tan(theta)sec2(theta)/(tan2(theta)+1)
=[itex]\int[/itex]4tan(theta)d(theta)
=-4ln(cos(theta))=-4ln(cos(arctan(x)))
thanks for the help, this problem is driving me crazy since it appears so simple.
edit: The answer is 2ln(x2+1)+C