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x-2/x
Solving integrals/ x-2/x

Integral of x-2/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  E           
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1
∫1e(x−2x) dx\int\limits_{1}^{e} \left(x - \frac{2}{x}\right)\, dx 
Integral(x - 2/x, (x, 1, E))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

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

      ∫(−2x) dx=−2∫1x dx\int \left(- \frac{2}{x}\right)\, dx = - 2 \int \frac{1}{x}\, dx

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

      So, the result is: −2log⁡(x)- 2 \log{\left(x \right)}

    The result is: x22−2log⁡(x)\frac{x^{2}}{2} - 2 \log{\left(x \right)}

  2. Add the constant of integration:

    x22−2log⁡(x)+constant\frac{x^{2}}{2} - 2 \log{\left(x \right)}+ \mathrm{constant}

The answer is:

x22−2log⁡(x)+constant\frac{x^{2}}{2} - 2 \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
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∫(x−2x) dx=C+x22−2log⁡(x)\int \left(x - \frac{2}{x}\right)\, dx = C + \frac{x^{2}}{2} - 2 \log{\left(x \right)}
Simplify
The graph
1.01.21.41.61.82.02.22.42.65-5
Plot the graph f(x)
The answer [src] 
       2
  5   e 
- - + --
  2   2
−52+e22- \frac{5}{2} + \frac{e^{2}}{2} 
=
= 
       2
  5   e 
- - + --
  2   2
−52+e22- \frac{5}{2} + \frac{e^{2}}{2} 
-5/2 + exp(2)/2
Numerical answer [src] 
1.19452804946532
1.19452804946532
The graph
Integral of x-2/x dx

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

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