Question

fund the exact length of the curve y=e^x, from x between 0 and 3

Answer 1

\[ \Large \int_0^3 \sqrt{1+e^{2x}}dx \]
yes ?

Answer 2

thats part of the answer but you have to make a u substitution or two and possibly use partial fractions

Answer 3

I would start with a trig substitution, maybe this will lead nowhere but let e^x=tan alpha

Answer 4

will that help?

\[ e^x= \tan \alpha \\
dxe^x = \sec^2{\alpha}d\alpha \longrightarrow dx=\sec^2\alpha \cot\alpha d\alpha \]