Question

converge or diverge: from 1 to infinty:
1/(3x+1)^2dx

Answer 1

@eliassaab medal? lol

Answer 2

convergent

Answer 3

please show how to do it

Answer 4

this one is easy to integrate...use u=3x+1

Answer 5

oh! hahaha.kk

Answer 6

wait im stuck

Answer 7

\[\frac{1}{(3x+1)^2}\le\frac{1}{x^2}\]

then

\[0\le\int\limits_{1}^{\infty}\frac{1}{(3x+1)^2}dx\le\int\limits_{1}^{\infty}\frac{1}{x^2}dx=\cdots\]

Answer 8

what zarkon said, although you know it converges because the degree of the denominator is 2 and the degree of the numerator is 0, and 2 - 0 > 1

Answer 9

wow, satellite73, is that atrick? how does that work?

Answer 10

not sure i would call it a trick, rather it is a fact