forgotten your Algebra I?
x/(6x-5) = 1/6 + 5/6 * 1/(6x-5)
Evaluate using long division.
The integral of x/6x-5 dx
How do I divide this?
2 answers
the way I read that is that you first want to divide x by 6x-5, and then integrate that series
using long division ....
x/(6x-5) = 1/6 + 5/(36x) + 25/(216x^2) + 125/(1296x^3 + ..
(a geometric series with a = 1/6 and r = 5/(6x)
so ∫x/(6x-5) dx
= ∫(1/6 + 5/(36x) + 25/(216x^2) + ...) dx
= (1/6)x + (5/36)lnx - 25/(216x) - 125/(2592x^2) - .....
using long division ....
x/(6x-5) = 1/6 + 5/(36x) + 25/(216x^2) + 125/(1296x^3 + ..
(a geometric series with a = 1/6 and r = 5/(6x)
so ∫x/(6x-5) dx
= ∫(1/6 + 5/(36x) + 25/(216x^2) + ...) dx
= (1/6)x + (5/36)lnx - 25/(216x) - 125/(2592x^2) - .....
1 answer