Solve the following integral using both the general substitution rule and integration by parts:

Question

anonymous · Answer

$$\int\limits_{0}^{1}e^{-\sqrt(x)}dx$$

anonymous · Answer

your suggestion disappeared... 
u= e^(-sqrt(x)) and dv=dx?

turingtest · Answer

yeah, it wasn't working for me though... maybe it will pay off and I just got lazy

anonymous · Answer

Yea I haven't gotten very far...

turingtest · Answer

I'm thinking$$u=e^{-x^{1/2}}\implies du=\frac12x^{-1/2}e^{-x^{1/2}}dx$$$$dv=dx\implies v=x$$$$\int e^{-x^{1/2}}dx=xe^{-x^{1/2}}-\int\frac12x^{1/2}e^{-x^{1/2}}dx$$

turingtest · Answer

$$u=e^{-x^{1/2}}\implies du=\frac12x^{-1/2}e^{-x^{1/2}}dx$$

turingtest · Answer

$$\int\frac12x^{1/2}e^{-x^{1/2}}dx=\int xdu=xu-\int udx$$nope, that's the end of it, we get 0=0 from that :P

turingtest · Answer

new idea:
start by substituting $$u=x^{1/2}$$then integrating by parts from the result. I think that will work.