Question

Calculus question - show that...

Answer 1

\[\int\limits(2e ^{2x}-5)/(e ^{2x}-5x)^{2/3}=3(e ^{2x}-5x)^{1/3} +C\]

Answer 2

\[
\int\frac{2e^{2x}-5}{(e^{2x}-5x)^{2/3}}dx
\\u=e^{2x}-5x,\ du=2e^{2x}-5dx
\\ \int u^{-2/3}du=3u^{1/3}+C=3(e^{2x}-5x)^{1/3}+C

\]