Question

integrate (e^5x)/[e^10x -e^5x]

Answer 1

\[\int\limits \frac{ e ^{5x} }{e ^{10x}-e ^{5x} }dx\]
put \[e ^{5x}=u,e ^{5x}*5 dx=du,dx=\frac{ 1 }{5 }du\]
\[also~\left( e ^{5x} \right)^{2}=u ^{2},e ^{10x}=u ^{2}\]
substitute and integrate after making partial fractions.

Answer 2

hmm.. so then I get (1/5)int[u/(u(u-1))] --> (1/5)int(u-1)^1 du = ln|e^5x -1| +C?

Answer 3

no
\[\frac{ 1 }{5 }\int\limits \frac{ du }{ u \left( u-1 \right) }\]

Answer 4

Oh, thanks that helps!

Answer 5

yw