Hey itshayley.
The derivative of ln(2x) is 1/x and it isn't the integral.
Try setting up dv = ln(2x) and u = x^(-2) [You have the v variables the wrong way around].
Hi all, I'm a little new here, but I hope you don't mind me joining your little community as I delve into Calculus II. I'd really like to learn to enjoy this class and be proficient in it. I hope you all will support me in this.
Directions: In Exercises 11-38, find the integral. (Note: Solve by the simplest method--not all require integration by parts.)
I tried making
dv=ln2x
v=1/2x
u=x^-2
du=-2/x^3
When plugging it into integral-calculator and Wolfphram Alpha I get nothing like my answer which was:
1/2x^3 + -1/4x^3 + c
For , you should let and . Then and . So:
There is a way to remember what to put in u and what to put in dv - it's "LIATE" - you choose for u whatever comes first in the list Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, Exponential. It's not foolproof, but it's a pretty good rule of thumb.
- Hollywood