Wednesday

April 16, 2014

April 16, 2014

Posted by **MS** on Friday, September 20, 2013 at 2:41am.

=[(log x)/a] + C.

The working in the book is

Int(1/ax)dx=1/a*Int(a/ax)dx

=[(log ax)/a]+C.

Which one is correct and where is the error in my working, if so?

- Calculus -
**Steve**, Friday, September 20, 2013 at 5:06amboth are correct

log ax = log a + log x

so, the loga/a is included in the C when you do it. The book probably did it their way to retain the appearance of (ax) as a function of x.

int(1/ax) dx let u = ax and you have

1/a int 1/u du

integrate that to get 1/a logu + C

= 1/a log(ax) + C

The C's are different, that's all.

FWIW, I prefer your way.

- Calculus -
**MS**, Friday, September 20, 2013 at 6:29amThank yoy very much Mr. Steve for making it so clear and easy.

**Related Questions**

Calculus - Integrate x dx/(1-x). I have proceeded thus- Int xdx/(1-x)=int -(x-1+...

Calculus - Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x^...

Calculus - Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x^...

Calculus - Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x^...

Calculus - Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x...

Calculus - int(dx/(x^2+9)) u = x/3 Use the indicated substitution (above) to ...

Calculus - Int tanx sec^2x dx can be taken as (by putting it in form of Int xdx...

Calculus - Can someone help me to evaluate these two integrals? INT dx/(x^2*sqrt...

Calculus - Center of Mass - Find the exact coordinates of the centroid given the...

Calculus - Find arc length of y=logx from x=1 to x=2. dy/dx)^2=1/x^2 arc length=...