Question

i need help solving integral e ^sqrt(x)/sqrt(x) with u substitution

Answer 1

id assume the most obvious sub is u=sqrtx

Answer 2

you should end up with 2u' e^u

Answer 3

can you pls show me how u got that

Answer 4

how "I" got it? or how youre spose to get it?

Answer 5

i got it by looking at the setup and realizing what i needed to do to make it uable

Answer 6

i mean i got du=1/2x-1/2

Answer 7

although i dont remember what to do next

Answer 8

1/2x^-1/2

Answer 9

u = sqrtx

du = 1/2sqrtx dx

2sqrtx du = dx

now substitute it in;

Answer 10

thats the part that confuses me

Answer 11

everywhere you see a sqrtx; put a u ; since u = sqrtx

Answer 12

everywhere you see a dx, replace it with 2sqrtx du since 2sqrtx du = dx

Answer 13

your simply replacing parts to clean up the scene

Answer 14

oh right

Answer 15

can you show me how u differentiated them

Answer 16

like how u wrote the origninal ones

Answer 17

i made it e^sqrt(x)*x^1/2

Answer 18

let u = sqrtx ; then deriva both sides

du = 1/2sqrtx dx as per the rules of derivatives ; rearrange so dx i all alone

Answer 19

when you bring somethng over the fraction bar, you negate the exponents

Answer 20

oh ya

Answer 21

2sqrtx du = dx ; but u = sqrtx

2u du = dx

Answer 22

e^sqrtx/sqrtx dx

replace parts

e^u/u 2u du

clean up

2e^u du

Answer 23

ok so i got integral of e^u *sqrt(x)-1/2 times dx which =2*sqrtx

Answer 24

where do i put 2sqrt x?

Answer 25

dx = 2sqrtx du replace it all

or you can see it as

dx
---- = 2 du
sqrtx

Answer 26

ook thanks i think i get it little more now

Answer 27

just keep at it; pull it all apart and replace all the things you can replace