!!helpp Urgent!! (1 Viewer)

[oh2sxc]

Ok I have one question...

Can someone show me how the primitive function for..

4lnx+4

comes out as 2[xlnx^2] ??

ta

 

[SoulSearcher]

Notice the derivative of xlnx
d/dx (xlnx) = lnx + 1
4lnx + 4 = 4(lnx + 1)
Therefore
int. [4lnx + 4] dx
= 4 * int. [lnx + 1]
= 4 * xlnx + C
= 2 * 2xlnx + C
= 2{x ln(x²)} + C, using the power rule, a*lnx = ln(x^a)

 

[oh2sxc]

hmmm i dont get the transition from

= 4 * int. [lnx + 1] there to..

= 4 * xlnx + C there.

thats the only part i dont get cheers man..

 

[SoulSearcher]

integral of [lnx + 1] dx = xlnx + C
Because we have shown that:
d/dx (xlnx) = lnx + x * 1/x
= lnx + 1

Does that help?

 

[oh2sxc]

ehhh kinda lets just hope I don't get it in my trial today eh

cheers heaps mate.