The Logarithmic Function....help? (1 Viewer)

[plshelp]

Ok this question is from Cambridge Mathematics 3 Unit Year 11:
Its on p.458 Ex.12D q:11 (in case anyone has already done this...)

How do we integrate 1/x(logx)?

Others: Integrate
1/sqrtx(sqrtx=1)
1/x(logx^2)

Can someone please show me how to integrate them? Maybe do one question and i'll probably be able to work out the rest....

Thanks heaps!

 

[cutemouse]

How do we integrate 1/x(logx)?

I=int 1/(x logx) dx

let u=log x, du/dx = 1/x

I= int 1/u du = log |u| +c = log | log x | + c