Question

Chapter Death

Answer 1

\[\frac{ 7-lnx }{ x(3+lnx) }dx\]

Answer 2

Integrate

Answer 3

What would ganeshie do...Sub u = lnx, du = 1/x dx

Answer 4

I guess you'll have to do long division as well

Answer 5

and maybe another substitution xD

Answer 6

What. No.

Answer 7

u sub -> long division -> another substitution

Answer 8

When I substitute, I get (7-u)/(3+u) *du

Answer 9

Yeah so do long division now

Answer 10

How do I deal with the remainder?

Answer 11

What did you get?

Answer 12

7/3 R 4/3u

Answer 13

Or just let \(u=3+\ln x\). The integral then becomes \(\displaystyle \int\frac{10-u}{u}\,du = \int\frac{10}{u}-1\,du\)

Answer 14

INTERESTING

Answer 15

Integrals are interesting indeed. XD

Answer 16

\[\int\limits \frac{ 10 }{ u+3 }-1 du\]

Answer 17

let t = u+3, dt = du

Answer 18

\[10 \int\limits \frac{ 1 }{ t }dt- \int\limits 1 du \implies 10\ln(lnx+3)-lnx+C\]