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xe^(1/x)
Solving integrals/ xe^(1/x)

Integral of xe^(1/x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01e1xx dx\int\limits_{0}^{1} e^{\frac{1}{x}} x\, dx 
Integral(x*E^(1/x), (x, 0, 1))
Detail solution

  1. Let u=1xu = \frac{1}{x}.

    Then let du=−dxx2du = - \frac{dx}{x^{2}} and substitute −du- du:

    ∫(−euu3) du\int \left(- \frac{e^{u}}{u^{3}}\right)\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫euu3 du=−∫euu3 du\int \frac{e^{u}}{u^{3}}\, du = - \int \frac{e^{u}}{u^{3}}\, du

        UpperGammaRule(a=1, e=-3, context=exp(_u)/_u**3, symbol=_u)

      So, the result is: E⁡3(−u)u2\frac{\operatorname{E}_{3}\left(- u\right)}{u^{2}}

    Now substitute uu back in:

    x2E⁡3(−1x)x^{2} \operatorname{E}_{3}\left(- \frac{1}{x}\right)

  2. Add the constant of integration:

    x2E⁡3(−1x)+constantx^{2} \operatorname{E}_{3}\left(- \frac{1}{x}\right)+ \mathrm{constant}

The answer is:

x2E⁡3(−1x)+constantx^{2} \operatorname{E}_{3}\left(- \frac{1}{x}\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | x*\/ E  dx = C + x *expint|3, ---|
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∫e1xx dx=C+x2E⁡3(−1x)\int e^{\frac{1}{x}} x\, dx = C + x^{2} \operatorname{E}_{3}\left(- \frac{1}{x}\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1e2855e284
Plot the graph f(x)
The answer [src] 
     Ei(1)
oo - -----
       2
−Ei⁡(1)2+∞- \frac{\operatorname{Ei}{\left(1 \right)}}{2} + \infty 
=
= 
     Ei(1)
oo - -----
       2
−Ei⁡(1)2+∞- \frac{\operatorname{Ei}{\left(1 \right)}}{2} + \infty 
oo - Ei(1)/2
Numerical answer [src] 
3.92310711940104e+4333645441173067294
3.92310711940104e+4333645441173067294
The graph
Integral of xe^(1/x) dx

    Use the examples entering the upper and lower limits of integration.

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