Question

whats the integral of e^(3sqrt(x))?

i think i'm supposed to use substitution but i don't know what to substirute, i tried u= x^(1/3) but it didn't work out, please help!

Answer 1

Did you try letting u = 3sqrt x?
x = (1/9)u^2
dx = (2/9) u du
Now the integral becomes the integral of
(2/9) u e^u du.
You will still need another step. I suggest using integration by parts.

I get (2/9)[ u e^u - e^u] + C
= (2/9)[3sqrtx e^(3sqrtx) - e^(3sqrtx)] + C
but check my numbers. I make mistakes all the time.