Question

Integral of dx/1+4x^2?

Answer 1

\[\int\limits \frac{ dx }{ 1+4x ^{2} }\]

Answer 2

@e.mccormick @jim_thompson5910

Answer 3

check out this table of integrals

http://integral-table.com/

look under "Integrals of Rational Functions"

Answer 4

You'll have to do a bit of substitution though. Let u = 2x, so u^2 = 4x^2

Answer 5

oh ok

Answer 6

so u=2x

Answer 7

don't forget to calculate du/dx and somehow figure out a way to replace dx as well

Answer 8

\[\frac{ 1 }{ 2 }\int\limits \frac{ 1 }{ 1+u ^{2} }du \]

Answer 9

looks good

Answer 10

now you use that table

Answer 11

sorry my internet just crashed

Answer 12

thats fine

Answer 13

\[\frac{ 1 }{ 2 }\tan ^{-1}u\]

Answer 14

recall that you let u = 2x, so replace u with 2x and don't forget the +C

Answer 15

also, say arctan(u) and NOT arctan u

the parenthesis help show you where the function ends

Answer 16

\[\frac{ 1 }{ 2 }\arctan(2x) +C\]

Answer 17

good

Answer 18

you nailed it

Answer 19

ok, thanks

Answer 20

np

Answer 21

im not good with trigonometric functions