Integrate (1/x)(Sqrt(x))

[Soko]

Hello all,

I am stuck on trying to integrate:

(1/x)(sqrt(x))

I came up with:

ln (x) ((2x^(3/2))/3) + C

The problem with that is I am just integrating both formulas and them sticking them together which I am guessing is wrong.

Can anyone help?

Thank you.

 

[Soko]

Ok, just spoke to a colleague who suggested an alternative way.

Turn (1/x) into x^(-1)
Turn Sqrt(x) into x^(1/2)

Times those two together = x^-(1/2)

Integrate that and get 2sqrt(x) + C

Is that along the right lines?

 

[JohnZ]

correct

 

[Deleted member 4993]

Ok, just spoke to a colleague who suggested an alternative way.

Turn (1/x) into x^(-1)
Turn Sqrt(x) into x^(1/2)

Times those two together = x^-(1/2)

Integrate that and get 2sqrt(x) + C

Is that along the right lines?

That is the easiest and most direct way.

As for your method of integration of products, you may have been thinking about the product rule of integration - which is slightly more complicated than the way you had applied!

 

[Soko]

Thank you guys, appreciate the feedback. Wish I found this website a long time ago.