need a quick reminder on how to do this simple integration, i keep confusing it with something else..


integral of dx/5x ??

Is it ln (5x) or (1/5) ln (5x)


dx/dt - 5x = 0

This post was edited by FamilyGuyViewer on Feb 2 2016 04:02pm

Integral of dx/5x is (1/5) ln(x)


The derivative of ln(x) = 1/x
The derivative of ln(5x) = 1/x

This is because:

ln(5x) = ln(5) + ln(x) = A constant + ln(x)

So the derivative is 0 + 1/x

This post was edited by RzChaos on Feb 2 2016 05:37pm

But also, the derivative is the derivative inside the parenthesis divided by the what's in the parenthesis

if the integral of dx/5x is (1/5) ln(x)... then why is the derviative 1/x..

Not sure I'm understanding your question?

Integral (1/5x) = (1/5) * Integral (1/x) = 1/5 * ln(x)

Whoops, meant to edit.

This post was edited by RzChaos on Feb 3 2016 07:28pm

ok but what about this differential equation,,

dx/dt = 5x

im either getting ln x = 5t + constant

or

(1/5) ln 5x = t + constant

dx/dt = 5x
1/(5x) dx = dt

Integral (1/(5x)dx) = Integral(dt)
1/5 Integral(1/x * dx) = Integral (dt)

1/5 * ln(x) = t + Constant

So yes, your first one was correct.

This post was edited by RzChaos on Feb 3 2016 08:21pm

what if u dont factor the 1/5 constant out.. wouldnt it still be ln 5x?

Factoring out the 1/5 doesn't change the answer. It just makes it easier to understand.

Not sure what you're getting hung up on...Maybe try these two websites and throw some integrals/derivatives into the calculator. It will try and break down each step for you.

http://www.integral-calculator.com/

http://www.derivative-calculator.net/


Think about this: ln(5x) = ln(5) + ln(x). ln(5) is a constant. When you take an integral you're not going to add in a constant as well as doing the "+ C". The ln(5) portion that you're trying to throw in there is already included in the "+C".




Yes, but that still doesn't change the answer.

derivative (ln(5x)) = 1/(5x) * derivative(5x) = 1/(5x) * 5 = 1/x

This post was edited by RzChaos on Feb 3 2016 08:39pm