Calculus1
9 Online
OpenStudy (anonymous):
Indefinite Integral
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OpenStudy (anonymous):
u=x-2
du =dx
OpenStudy (rational):
so many folks eager to help you :)
OpenStudy (anonymous):
\[\int\limits_{}^{}\frac{ x }{ \sqrt{x+1} }\]
OpenStudy (anonymous):
dx
OpenStudy (anonymous):
u=x+1 hahahaa
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OpenStudy (anonymous):
yeah but then what?
OpenStudy (anonymous):
du = dx
OpenStudy (anonymous):
x =? :)
OpenStudy (anonymous):
x = u-1
OpenStudy (anonymous):
boom boom boom
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OpenStudy (anonymous):
boom got it :D
OpenStudy (anonymous):
thx batman
OpenStudy (anonymous):
\[\int\limits \frac{ u-1 }{ \sqrt{u} }du\]
OpenStudy (anonymous):
Oh alright :)
OpenStudy (anonymous):
thx everyone actually XOXO
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OpenStudy (anonymous):
What did you get as an answer?
OpenStudy (rational):
dont ask, answer is something unpleasant i suppose ;)
OpenStudy (luigi0210):
And yw ;)
OpenStudy (anonymous):
Not too bad :), I can show the steps if you want.
OpenStudy (anonymous):
i got [2(x+1)^(5/2)]/5 - [2(x+1)^(3/2)]/3 + C
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OpenStudy (anonymous):
Not quite
OpenStudy (anonymous):
wha?
OpenStudy (anonymous):
i combined (u-1)(u)^1/2 before integrating
OpenStudy (anonymous):
so u^3/2 -u^1/2
OpenStudy (anonymous):
then i integrated that
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OpenStudy (anonymous):
and imported u = x+1 for it
OpenStudy (rational):
u^(1/2) - u^(-1/2)
OpenStudy (anonymous):
\[\int\limits \left( \sqrt{u}-\frac{ 1 }{ \sqrt{u} } \right)du\]
OpenStudy (anonymous):
ahhh you're very right..
OpenStudy (anonymous):
darn
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OpenStudy (anonymous):
:)
OpenStudy (anonymous):
\[\huge \frac{ 2 }{ 3 }(x-2)\sqrt{x+1}+C\]
This should be your final answer.
OpenStudy (anonymous):
thats what WFA gave me too.. but it still doesn't look like that >.<
OpenStudy (anonymous):
\[\huge \int\limits \sqrt{u}du-\int\limits \frac{ 1 }{ \sqrt{u} }du\]
\[\huge \frac{ 2u ^{3/2} }{ 3 }-2\sqrt{u}+C\]
\[\huge \frac{ 2 }{ 3 }(x+1)^{3/2}-2\sqrt{x+1}+C\]
\[\Huge \frac{ 2 }{ 3 }(x-2)\sqrt{x+1}+C\]
OpenStudy (anonymous):
Alright, I gtg now, good night and take care :).
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OpenStudy (anonymous):
GOT IT!