Posted by Sean on Sunday, March 16, 2008 at 7:47am.
I'm supposed to find the expression 'y', when
(x^2+100)y'=23
When y(10sqrt(3))=0
Also, I have to find the indefite integral
of
xsqrt(19x7), using integration tables in the back of the book "Calculus of a Single Variable, 8th Edition." Tables are in appendix B
I used the formula
[2/[b(2n3)]]*([u^n]*(a+bu)^[3/2]na[integral of [u^(n1)sqrt[a+bu]]]
I've used
a=7
b=19
u=x
du=xd
But it doesn't seem to work.

Calculus III  Count Iblis, Sunday, March 16, 2008 at 10:37am
Unless you really have to finish a problem in a hurry, never use integration tables or other tools for problem solving. Only use them to very the solution when you are done.
(x^2+100)y'=23 >
dy/dx = 23/[x^2 + 100] >
y = Integral of dy =
Integral of 23 dx/[x^2 + 100], looks like an arctan to me.
Integral of x sqrt(19x7)dx ?
Write the integral in terms of functins you do know the inegral of. Rewrite the factor of x as follows:
x = 1/19 (19 x) =
1/19 (19 x  7 + 7) =
1/19 (19 x  7) + 7/19
I think you'll now see the answer. These sorts of tricks cannot be learned by just looking in integral tables.

Calculus III  Sean, Sunday, March 16, 2008 at 11:12am
I got the first one, thanks for that.
But on the second one, are you saying that x=(1/19)*(19x7)+(7/19)?
If so, would I just multiply the entire thing out, or what?
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