Question

integral of -e^sqrt(x)

Answer 1

Meant to write - must use only substitution!

My reasoning:
u=sqrt{x}
du = \[1/\sqrt{x}\] dx
so dx = \[2\sqrt{x} du\]

so you should now be finding the integral of \[2\sqrt{x}e ^{\sqrt{x}}\]

which should you \[- 4e ^{\sqrt{x}}/3\sqrt{x}\]

however, this is wrong...answer is \[-2e ^{\sqrt{x}}(\sqrt{x}-1)\]

How can I solve this?

Answer 2

@mukushla

Answer 3

\[\int\limits{e^{\sqrt x}}dx\]
let u= sqrtx
du=1/2sqrt(x)dx
so\[dx=2 \sqrt xdu\]and since u=sqrtx\[dx=2udu\]

Answer 4

now substitute, integral becomes\[\int\limits{2e^u udu}\]

Answer 5

now do it byparts

Answer 6

@lalaly read the second comment , he said that "Must use only substitution"

Answer 7

oh ok

Answer 8

actually what lalaly did and so the asker himself (except losing the track of sub) is right, we cant find a way to get that answer with a direct substitution

Answer 9

ok thanks!!