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sin(e^x)
Solving integrals/ sin(e^x)

Integral of sin(e^x) dx

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The solution

You have entered [src] 
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∫01sin⁡(ex) dx\int\limits_{0}^{1} \sin{\left(e^{x} \right)}\, dx 
Integral(sin(E^x), (x, 0, 1))
Detail solution

  1. Let u=exu = e^{x}.

    Then let du=exdxdu = e^{x} dx and substitute dudu:

    ∫sin⁡(u)u du\int \frac{\sin{\left(u \right)}}{u}\, du

      SiRule(a=1, b=0, context=sin(_u)/_u, symbol=_u)

    Now substitute uu back in:

    Si⁡(ex)\operatorname{Si}{\left(e^{x} \right)}

  2. Now simplify:

    Si⁡(ex)\operatorname{Si}{\left(e^{x} \right)}

  3. Add the constant of integration:

    Si⁡(ex)+constant\operatorname{Si}{\left(e^{x} \right)}+ \mathrm{constant}

The answer is:

Si⁡(ex)+constant\operatorname{Si}{\left(e^{x} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫sin⁡(ex) dx=C+Si⁡(ex)\int \sin{\left(e^{x} \right)}\, dx = C + \operatorname{Si}{\left(e^{x} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
-Si(1) + Si(e)
−Si⁡(1)+Si⁡(e)- \operatorname{Si}{\left(1 \right)} + \operatorname{Si}{\left(e \right)} 
=
= 
-Si(1) + Si(e)
−Si⁡(1)+Si⁡(e)- \operatorname{Si}{\left(1 \right)} + \operatorname{Si}{\left(e \right)}
Упростить
Numerical answer [src] 
0.874957198780384
0.874957198780384
The graph
Integral of sin(e^x) dx

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

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