# Finding the area in calculus?

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

### 6 Answers

- Ian HLv 71 year ago
∫[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.

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- az_lenderLv 71 year ago
Google "logarithmic integral calculator" and

select the keisan.casio.com link,

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

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- ?Lv 61 year ago
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.

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