Question

integral of -6dx / 3+12x^2

Answer 1

Hint: The denominator factors into 3(1+4x^2), so you can pull a 1/3 out of the integral, and you are left with 1+4x^2 in the denominator.

But 1+4x^2 can be written as 1+ (2x)^2. Does this form of 1+ u^2 look familiar?

Answer 2

I SEE! But what do I do with the -6?

Answer 3

the -6 is in the numerator, that can be pulled outside of the integral.

Answer 4

so would the final answer be -2tan-1(2x) +C?

Answer 5

So you pull out the -6 and you also pull out the 1/3 from the denominator...so it's like you pulled out -2 in front of the integral.

Answer 6

More important is to see the "form" that this integral takes.

Answer 7

And I showed you the "form" it takes. You just have to recognize it.

Does it ring a bell?