Question

integral of -12 / (4+x^2) dx

Answer 1

I am not sure if this is would apply to a rule or not...but I get confused with these type of problems.

Answer 2

my brain is malfunctioning and I appear to be useless. I'm very sorry :P @Mashy can you help?

Answer 3

This appears to be a standard integral.. of the form

\[\int\limits_{}^{}\frac{1}{x^2+a^2} dx\]

u know the solution to that? or u want me to help u derive it?

Answer 4

could you help me?

Answer 5

sure.. use a trignometric substitution..

we ll derive the answer for the general case that i put up.. then u can apply it to your probelm

so what trignometric substituition can u think of?

Answer 6

would it be (1/a)tan-(a/u)+C?

Answer 7

ohw wow :P.. u directly gave the answer.. did u look it up somewhere? or u just did the whole thing in ur head? :D

Answer 8

it is a rule that the teacher gave us... so would it be -6xtan-(2/x) +C?

Answer 9

IT IS (X/2)?

Answer 10

well yea.. \[\int\limits_{}^{}\frac{1}{x^2+a^2}dx = \frac{\tan^{-1}(\frac{x}{a})}{a}\]

so just substitute now :P.. and see for yourself what the answer would be!

Answer 11

Yes, but then I would have to find a number that I can multiply so it can equal -12 on the top...

Answer 12

just take -12 out of the integral.. keep it separate and after integrating do the algebra!!..

Answer 13

and its (X/2)!

Answer 14

okay! so I get -6tan-(x/2) +C

Answer 15

yes.. thats right!

Answer 16

YAY! THANK YOU!

Answer 17

your welcome!