Sunday, January 1, 2017

calculus - Integration by parts: u substitution case for ln(2x+1)


Integrate by parts: ln(2x+1)dx


This question has answers here and I was wondering about the last answer to the question which is the way I did it, got a different answer?


https://math.stackexchange.com/a/1598118/372659


Here is the answer,


Is doing u-substitution, and then integration by parts a wrong method here? Because in my textbook the answer there is a ones in the other answers.


Answer



You should find


[xln(2x+1)]x22x+1dx



=xln(2x+1)2x+112x+1dx


=xln(2x+1)x+12ln(2x+1)+C


=2x+12ln(2x+1)x+C


You can also put u=2x+1 to get


ln(u)du2=12(uln(u)u)+K =2x+12ln(2x+1)x12+K


with C=K1/2.


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...