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anonymous
 5 years ago
how do i integrate dx/sqrt(4x)
anonymous
 5 years ago
how do i integrate dx/sqrt(4x)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Have you tried u substition?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0substitution as in integration by parts?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for your question, do you mean \[\int\limits_{}^{}dx/\sqrt{4x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes thats exactly it. i am studying improper integrals so i need to find the regular integral first

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Think of the square root on the bottom not as a square root, but as \[(4x)^{1/2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You will, however, have to use a u substitution, which is different the integration by parts. Integration by parts is only necessary in situations with multiplication or division of things you cannot simplify

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0More explicitly, think of it as \[\int\limits_{}^{}(4x)^{1/2}dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay, so then when you say substitute you mean, take (4x) and substitute u. and then perform \[1/n+1\times u ^ {n+1} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry getting used to the equation typing

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0essentially yes. \[u = (4x)\], and \[du/dx = 1\]. Substitute in u and du, integrate the function I wrote above, and replace (4x) when you're done.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when doing u substitutions, you substitute u, then take the derivative of what you substituted, in this case (4x), for x, which = 1 in this case.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh i see. so what i have then would be \[1^{1/2}/{1/2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and that becomes (u^1/2)/1 * 2/1 which is 2sqrt u. and that becomes 2sqrt(4x) is that right?
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