Question

how to integrate e^2x ?

Answer 1

\[\int\limits_{}^{}e^xdx = e^x + c\]

Answer 2

\[\int\limits_{}^{}e^{2x}.dx = e^{2x}/2 + c\]

Answer 3

yes, but how?

Answer 4

explain.

Answer 5

differentiate rhs and see u will get the lhs

Answer 6

rhs?? lhs??

Answer 7

you could substitute to be more explicit
\[\alpha x=u\qquad\qquad\alpha \text d x=\text du\qquad\qquad \text dx=\frac{\text du}{\alpha}\]
\[\int e^{\alpha x}\text dx=\int e^{u}\frac{\text du}{\alpha}=\frac 1\alpha \int e^u\text du=\frac 1 \alpha e^u+c=\frac{e^{\alpha x}}{\alpha}+c\]

Answer 8

UnkleRhaukus is right
btw rhs and lhs are
right hand side & left hand side