Question

Calculus Integrals, Solve by Substitution.. (pic included)
http://dl.dropbox.com/u/16729527/calc9.jpg

Answer 1

the answer is apparantly ln|lnx| + c but i dont know how to that besides u = lnx and du = (1/x)dx

Answer 2

Just make that Substitution..

\[\ln(x) = u\]
\[\frac{1}{x}dx = du\]

Answer 3

\[\int\limits(\frac{1}{u}) du\]

Answer 4

And this will give you your answer..

Answer 5

but in some problems they get rid of du i dont see why keep it in this problem

Answer 6

Where??

Answer 7

integral of 2x(x^2 + 1)^23; u = x^2 + 1 du = 2xdx then integral of udu the answer ends up being ((x^2 + 1)^24)/24 + c

Answer 8

after substituting the question becomes u = x^2 + 1
2xdx=du or the question can be written as (x^2 + 1)^23(2x)dx
hence the question becomes u^23du on integrating we have 1/24 (u^24) +c
hence the answer ends up being ((x^2 + 1)^24)/24 + c