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Solving integrals/ (1/x)+y*exp(x)

Integral of (1/x)+y*exp(x) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
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∫01(yex+1x) dx\int\limits_{0}^{1} \left(y e^{x} + \frac{1}{x}\right)\, dx 
Integral(1/x + y*exp(x), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫yex dx=y∫ex dx\int y e^{x}\, dx = y \int e^{x}\, dx

      1. The integral of the exponential function is itself.

        ∫ex dx=ex\int e^{x}\, dx = e^{x}

      So, the result is: yexy e^{x}

    1. The integral of 1x\frac{1}{x} is log⁡(x)\log{\left(x \right)}.

    The result is: yex+log⁡(x)y e^{x} + \log{\left(x \right)}

  2. Add the constant of integration:

    yex+log⁡(x)+constanty e^{x} + \log{\left(x \right)}+ \mathrm{constant}

The answer is:

yex+log⁡(x)+constanty e^{x} + \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
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∫(yex+1x) dx=C+yex+log⁡(x)\int \left(y e^{x} + \frac{1}{x}\right)\, dx = C + y e^{x} + \log{\left(x \right)}
Simplify
The answer [src] 
oo + E*y
ey+∞e y + \infty 
=
= 
oo + E*y
ey+∞e y + \infty 
oo + E*y

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

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