Question

Evaluate the definite integral: (dx/(x(1+ln(x))) from 1 to e^7.

Answer 1

let u = lnx
then du = dx/x

∫1/[x*(lnx+1] dx
= ∫(1/(u+1) du
= ln(u+1) + C
= ln[lnx+1)] + C

When x = 1, the indefinite integral is 0
When x =e^7, the indefinite integral is ln8. The C terms can be ignored since they cancel out.

ln8 is the answer