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Solving integrals/ (1-x^(-2))

Integral of (1-x^(-2)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫01(1−1x2) dx\int\limits_{0}^{1} \left(1 - \frac{1}{x^{2}}\right)\, dx 
Integral(1 - 1/x^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dx=x\int 1\, dx = x

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

      ∫(−1x2) dx=−∫1x2 dx\int \left(- \frac{1}{x^{2}}\right)\, dx = - \int \frac{1}{x^{2}}\, dx

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

        ∫1x2 dx=−1x\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}

      So, the result is: 1x\frac{1}{x}

    The result is: x+1xx + \frac{1}{x}

  2. Add the constant of integration:

    x+1x+constantx + \frac{1}{x}+ \mathrm{constant}

The answer is:

x+1x+constantx + \frac{1}{x}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(1−1x2) dx=C+x+1x\int \left(1 - \frac{1}{x^{2}}\right)\, dx = C + x + \frac{1}{x}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-5000000050000000
Plot the graph f(x)
The answer [src] 
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−∞-\infty 
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−∞-\infty 
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Numerical answer [src] 
-1.3793236779486e+19
-1.3793236779486e+19

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

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