Question

what's the indefinite integral of y=(e^(x/2)) / (sqrtx) ?

Answer 1

i meant square root of x in the sqrtx part

Answer 2

this is not an elementary integral
what class is this?

Answer 3

i'm in precalculus honors

Answer 4

precalculus and integrals?
lol

Answer 5

idk my teacher wants us to learn more caluclus stuff for next year....

Answer 6

i don't see how to do this
it failed at integral by parts

Answer 7

I'm working on it....gimme a sec

Answer 8

\[\int\limits_{}^{}\frac{e^{\frac{x}{2}}}{\sqrt{x}} dx\]
? right?

Answer 9

ya! that's the question

Answer 10

and part 2 of the question is find the derivative

Answer 11

i still say there is no elementary way to evaluate this
i would like someone to evaluate it, but im not sure how many people on here no complex analysis or whatever else you need for this

Answer 12

oh... thanks for working on this problem anyway :)

Answer 13

blue hows it going?

Answer 14

Hmm..not great, you may be right...I'll let you know if I have a breakthrough.

Answer 15

lol gl i think i will leave this site up all night and check it randomly to see if anyone answers this

Answer 16

Blue were you trying to use integration by parts

Answer 17

You're right, you can't do it. I put it into wolfram. One of the components of the answer is the erf function.

Answer 18

Yes zeal, first by parts and then by u substitution with u=sqrt(x), then x=u^2, etc...but then you just end up with e^(0.5u^2) in the integrand and it gets you nowhere. I honestly find it kind of hard to believe that they'd give you this, or any other, integral in a precalc class.

Answer 19

thank you guys for working on this problem...! btw, is finding the derivative for y=(e^(x/2)) / (sqrtx) also impossible too?

Answer 20

No, finding the derivative of that is pretty straightforward...just gotta follow some rules (chain, quotient, power, etc).

Answer 21

i substituted sqrt of x first... is that correct?

Answer 22

Hmm? No substituting for derivatives. Have you learned the quotient or chain rules yet?

Answer 23

ya... i got [(e^(x/2))*(sqrt of x)]/2 + [(e^(x/2)) / (2*sqrt of x}] as the answer.... is that right?

Answer 24

(e^(x/2))'=1/2*e^(x/2)
(x^(1/2))'=1/(2sqr{x})
so we need to use quotient rule since we have f/g
quotient rule: (f/g)'=(f'g-fg')/g^2
=(1/2*e^(x/2)*x^(1/2)-e^(x/2)*1/(2sqrt{x}))/x
and we can make this look nice by getting rid of the compund fraction

Answer 25

multply top and bottom by 2sqrt{x} and that will do the trick
i have to go to bed
good night

Answer 26

thanks!

Answer 27

oh i forgot about that g^2