OpenStudy (anonymous):

integral of -e^sqrt(x)

4 years ago
OpenStudy (anonymous):

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?

4 years ago
OpenStudy (loser66):

@mukushla

4 years ago
OpenStudy (lalaly):

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

4 years ago
OpenStudy (lalaly):

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

4 years ago
OpenStudy (lalaly):

now do it byparts

4 years ago
OpenStudy (loser66):

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

4 years ago
OpenStudy (lalaly):

oh ok

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

ok thanks!!

4 years ago