Question

how do you integrate e^(-sqrt(x))/(4 sqrt(x)) dx

Answer 1

very carefully :)

Answer 2

e^(-sqrt(x))
---------- dx eh.... can we make a u sub and say...
4sqrt(x) u = sqrt(x) ?

Answer 3

yes i used u = -sqrt(x)

Answer 4

du = 1/2sqrt(x) dx

dx = du 2sqrt(x)

Answer 5

okay

Answer 6

2sqrt(x) e^-u du
--------------- ....murmur
4u

Answer 7

now factor out 1/2?

Answer 8

still have that sqrt(x) hanging in there causing troubles

Answer 9

or can we simply equate that to a -u?

Answer 10

e^-u du
----------- then right?
2

Answer 11

wait what?

Answer 12

2sqrt(x) = 2u right? since u = sqrt(x)

Answer 13

right

Answer 14

2u 1
-- = -- if its doable
4u 2

Answer 15

okay

Answer 16

then all we are missing is a -1 to integrate with.... so I propose this set up:

-(1/2) [S] -e^-u du

Answer 17

which integrates to:

-e^-u
------ +C lets check that thought and see if it works
2

Answer 18

-e^-sqrt(x)
--------- derives to what?
2

Answer 19

- 1 -e^-sqrt(x)
------- * -------------- looks good to me
2sqrt(x) 4

Answer 20

thanks

Answer 21

i got lucky lol ;) youre welcome

Answer 22

I just did this problem yesterday for calc, I was going to help but Amitre is far better at explaining then I am.

Answer 23

:) hey bobby

Answer 24

:) i just winged it; threw what i had at it to see what stuck ;)

Answer 25

Woah who is this??

Answer 26

lols chelsea

Answer 27

fādāi means day dream in chinese