integration problem: integrate 4/(1+4x^2)dx

[edressler]

Hi there,

I'm trying to determine the steps for integrating the following problem: integrate 4/(1+4x^2)dx

I was able to find the answer: 2tan^-1(2x) + C

I think this has something to do with this rule: Int of 1/(x^2+1)dx = tan^-1(x) + C

Would anyone mind running down how that rule is related to the above answer?

Thanks,

-edressler

 

[Deleted member 4993]

Hi there,

I'm trying to determine the steps for integrating the following problem: integrate 4/(1+4x^2)dx

I was able to find the answer: 2tan^-1(2x) + C

I think this has something to do with this rule: Int of 1/(x^2+1)dx = tan^-1(x) + C

Would anyone mind running down how that rule is related to the above answer?

Thanks,

-edressler

\(\displaystyle \displaystyle{\int \dfrac{4 dx}{1+4x^2}}\)

Substitute

u = 2x → du = 2 dx

\(\displaystyle = \displaystyle{2 \ \int \dfrac{ du}{1+u^2}}\)

continue and back-substitute

 

[edressler]

Thanks

\(\displaystyle \displaystyle{\int \dfrac{4 dx}{1+4x^2}}\)

Substitute

u = 2x → du = 2 dx

\(\displaystyle = \displaystyle{2 \ \int \dfrac{ du}{1+u^2}}\)

continue and back-substitute

Thanks!