Posted by **Back against the wall** on Friday, November 26, 2010 at 9:38pm.

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

- Calculus 1 -
**drwls**, Friday, November 26, 2010 at 10:16pm
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

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