Heklp with an integral involving the exp function

[xnr]

Hi everyone

I've been dealing with a rather difficult (at least for me) integration problem which I am not able to find in integration tables I've been consulting.
After a variable transformation I ended up with the following sets of integrals:

$$\\int$$ e$$^{y}$$/y$$^{2}$$dy from 0 to t (t is not infinity) and

$$\\int$$ e$$^{y}$$/y$$^{3}$$dy also from 0 to t and

(sorry I could not get the integral symbol to work, so I used int instead)

thanks
xnr

 

[HallsofIvy]

Neither of those looks convergent (at 0) to me.

 

[g_edgar]

As Halls said, they diverge at 0. The indefinite integral of exp(y)/y is a non-elementary function known as the "exponential integral" function. Your two integrals may be expressed in terms of the exponential integral function using integration by parts.