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
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