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x-(1/x)
Solving integrals/ x-(1/x)

Integral of x-(1/x) dx

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The solution

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∫13(x−1x) dx\int\limits_{1}^{3} \left(x - \frac{1}{x}\right)\, dx 
Integral(x - 1/x, (x, 1, 3))
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:

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

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

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

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

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫(x−1x) dx=C+x22−log⁡(x)\int \left(x - \frac{1}{x}\right)\, dx = C + \frac{x^{2}}{2} - \log{\left(x \right)}
Simplify
The graph
1.03.01.21.41.61.82.02.22.42.62.805
Plot the graph f(x)
The answer [src] 
4 - log(3)
4−log⁡(3)4 - \log{\left(3 \right)} 
=
= 
4 - log(3)
4−log⁡(3)4 - \log{\left(3 \right)} 
4 - log(3)
Numerical answer [src] 
2.90138771133189
2.90138771133189
The graph
Integral of x-(1/x) dx

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

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