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 Nov10 awarded Notable Question Jul2 awarded Curious Oct30 awarded Popular Question Aug12 comment How do we calculate this exponential integral if we change limit from $\infty$ to $x_1$ It doesn't even have a $\sinh$, $\cosh\dots$. It is not programable. Can you recommend any good calculator to calculate integrals? Aug12 comment How do we calculate this exponential integral if we change limit from $\infty$ to $x_1$ Well my calculator lacks it :) Aug12 comment How do we calculate this exponential integral if we change limit from $\infty$ to $x_1$ Does this mean this can only be solved using numerical methods? Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one Knowing this rule can save A LOT of integration per partes :) Aug12 comment How do we calculate this exponential integral if we change limit from $\infty$ to $x_1$ Thank you. Is the error function really necessary :/ ??? Aug12 revised How do we calculate this exponential integral if we change limit from $\infty$ to $x_1$ deleted 1 characters in body Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one I know that $\int_{-\infty}^0 = - \int_{0}^{-\infty}$ but if i want to know what happens if i insert $-x$ instead of $x$ i have to check what function i have. In my case it is odd so i should get the change in sign also... Does this mean that $\int_{-\infty}^{0}=-\int_{\infty}^{0}$ AND $\int_{0}^{\infty}=-\int_{0}^{-\infty}$ ??? Aug12 comment How do we calculate this exponential integral if we change limit from $\infty$ to $x_1$ I din't change it. I have to solve the later integral which has $x_1$ for limit. But i found the first integral in the mathematics manual. Aug12 asked How do we calculate this exponential integral if we change limit from $\infty$ to $x_1$ Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one So to solve these types of problems we use the known integral (which is not definite): $\int x e^{-ax^2}dx= - \frac{1}{2a}e^{-ax^2}dx$ again and again using the perpartes. If i understood right this is the philosophy behind this case. Does this formula has a derivation? Please point me to it. Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one But $d/dx\,e^{ax^2}=2ax\,e^{ax^2}$ I don't understand why above isn't true... Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one One more thing. Isn't it $\int e^{ax^2}dx = \frac{1}{2ax}e^{ax^2}$? Aug12 accepted Some exponential integrals - I need algebraical solution besides my graphical one Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one I like hints like this one :) Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one Your case is for the $x$ what about for the $x^2$? Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one Oh i forgot to mention that $n,~a \in \mathbb{N}$. Aug12 comment Some exponential integrals - I need algebraical solution besides my graphical one I would like to analytically show, that they equal 0. Check my Edited Question. I was thinking to solve them using the relation described there, but i get spapped limits and a negaitve sign... Long story short, I need to know what are the relations between $$\int\limits_{0}^{\infty} dx \qquad \int\limits_{0}^{-\infty} dx \qquad \int\limits_{\infty}^{0} dx \qquad \int\limits_{-\infty}^{0}$$