Question

Evaluate:

`int1/(xsqrt(logx)) dx`

Answer 1

Let I = `int1/(xsqrt(log x)) dx = int1/(sqrt(log x)) · 1/x dx`

Put log x = t

∴ `1/x dx = dt`

∴ `I = int 1/(sqrtt) dt`

= `int t^(-1"/"2)  dt`

= `(t^(1"/"2))/((1/2)) + c`

= `2 sqrtt + c`

 = `2sqrt(logx) + c`