# Finding the area in calculus?

Find the area under the curve y = 1/Inx from x = 2 to 5

Relevance
• ∫[1/ln(x)]dx has no simple function form

If you just require a value for

I ={x: 2 to 5)} ∫[1/ln(x)]dx it is ~ 2.58942453 (graphic calculator)

Wolfram Alpha gives it as Li(5) – Li(2) where

Li represents a special function, the logarithmic integral. It gives good approximation to the prime-counting function, and if you scroll down to series in this link you can find a rapidly convergent series equivalent due to Ramanujan.

https://en.wikipedia.org/wiki/Logarithmic_integral...

• Google "logarithmic integral calculator" and

to find li(5) and li(2),

then subtract li(5) - li(2) to get the answer.

A one-trapezoid use of the trapezoidal rule gives around 3.1;

three trapezoids gives 2.66;

six trapezoids gives 2.61;

lots and lots of trapezoids will get close to 2.58

• X=2(x) + 2(y) ghjiugnkijn

• Doesn't 1/ln(x) integrate into something really nice like e? I think it takes u-sub. Been a billion years since grammar school.