How do I integrate (x-2)Ln(3x)???

Answer 1

(1/4)*x*(-x+2*(x-4)*ln(3*x)+8)

Answer 2

There is no analytical solution for an integral of a natural logarithm, and i learnt this the hard way, sitting in an exam trying to work out an analytical integral for a ln function forgetting the question was aimed at using reduction formulae...

therefore you must use reduction formulae to reduce the original integral into a function of a new integral where the value of the new integral can be worked out... This is what all the people before me have done by using integration by parts...

its pointless me typing the same as what everyone has done before me again, but i hope that goes some way to explaining the logic behond using integration by parts on this sort of integral.

Answer 3

Note :- x^2 means x square.

First u have to open the brackets. Then you will get
xln(3x)-2ln(3x).
Integrate first term using integration by-parts.
If u know how to do that then u will get
((x^2)ln(3x))/2 - x^2/2.
Then for the 2nd term, u will again have to use int. by-parts as the function is log. Then u will get
- (2xln(3x) - 2x)
Open the bracket and put them together. I have ignored the constant term that is at the end of each integration.

Answer 4

I would distribute the ln(3x) and then use intergration by parts. You can find a table of integrals for the integral of ln(3x) either in your text-book or via google search.

Answer 5

By parts
intg (u dv)= uv - intg(v du)

Answer 6

input (x-2)Log[E,3x]

http://integrals.wolfram.com/index.jsp

Answer 7

http://www.safeshop.org.uk/

Answer 8

Do you speaka la english?!!