Integrating 1/x*e^x dx from 0 to s, how to do it

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Hi

I have an integral as follows,

int((1/x)exp(-x),x,0,s)

I want to integrate from [0,s).

My question is how to integrate without including s as the upper bound.

Any help will be appreciated
 
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Integrate from [0,s-a] in the limit as a -> 0?
 


Hey

Thanks for the reply.

If the integral is the lower gamma incomplete function, which is

int(exp(-t)*t^(a-1),t,0,x)

how would I be able to evaluate the integral between [0,x-a) as a->0 ?
 


Feldoh said:
Integrate from [0,s-a] in the limit as a -> 0?

well u are right

but i don't know, his question doest sound too sensible to me

then by anser u gave it obviously means changing parameters of integration
 


Hi sachinism

I hope I cleared up my question with my last post.

Any help will be great
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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