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## Homework Statement

Find the value of the constant C for which the following integral converges. Evaluate the integral for this value of C:

[tex]\int[/tex] [tex]\frac{x}{x^2+1}[/tex] - [tex]\frac{C}{3x+1}[/tex]dx from 0 to infinity

## Homework Equations

## The Attempt at a Solution

[tex]\stackrel{lim}{t->inf.}[/tex] [tex]\int[/tex] [tex]\frac{x}{x^2+1}[/tex] dx - [tex]\stackrel{lim}{t->inf.}[/tex] [tex]\int[/tex] [tex]\frac{C}{3x+1}[/tex] dx

for (x^2/(x^2+1):

u = x^2 + 1

du = 2xdx

[tex]\stackrel{lim}{t->inf.}[/tex] (1/2)ln(u) dx

[tex]\stackrel{lim}{t->inf.}[/tex] (1/2)ln(x^2+1) ] [tex]\stackrel{t}{0}[/tex]

[tex]\stackrel{lim}{t->inf.}[/tex] (1/2)ln(t^2+1)

Now I am unsure of what to do. How do I know the limit of this first half? How can I use it to help me find what value of C will make it convergent? Your time and effort is greatly appreciated in helping me understand this \

***Please note (I don't know how to format limits haha) that I mean the limit as t approaches infinity! Thanks!***