Question

Find the integral of (2x-1)/(x-1)^2 dx.

Answer 1

I suppose we have to split it into the sum of two integrals?

Answer 2

How?

Answer 3

\[\int\frac{2x}{(x-1)^2}dx-\int\frac1{(x-1)^2}dx\]

Answer 4

And then?

Answer 5

u=x-1

Answer 6

Integration by substitution

Answer 7

I mean, du=dx?

Answer 8

Yes

Answer 9

Wait don't split now

Answer 10

Split after substituting

Answer 11

\[\begin{array}{cl}
&\int\frac{2x-1}{(x-1)^2}dx\\
=&\int\frac{2u+1}{u^2}du\\
=&\int\frac2udu+\int\frac1{u^2}du
\end{array}\]

Answer 12

I suppose you can do it now?

Answer 13

I'll try.

Answer 14

Remember the power law (or however you call it): \(\Large\displaystyle\int x^ndx=\frac{x^{n+1}}{n+1}+C\)

Answer 15

I got it. Thanks.

Answer 16

no problem