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(x-1)/x^3
Solving integrals/ (x-1)/x^3

Integral of (x-1)/x^3 dx

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The solution

You have entered [src] 
  1         
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∫01x−1x3 dx\int\limits_{0}^{1} \frac{x - 1}{x^{3}}\, dx 
Integral((x - 1)/x^3, (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    x−1x3=1x2−1x3\frac{x - 1}{x^{3}} = \frac{1}{x^{2}} - \frac{1}{x^{3}}

  2. 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:

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

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

      ∫(−1x3) dx=−∫1x3 dx\int \left(- \frac{1}{x^{3}}\right)\, dx = - \int \frac{1}{x^{3}}\, dx

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

        ∫1x3 dx=−12x2\int \frac{1}{x^{3}}\, dx = - \frac{1}{2 x^{2}}

      So, the result is: 12x2\frac{1}{2 x^{2}}

    The result is: −1x+12x2- \frac{1}{x} + \frac{1}{2 x^{2}}

  3. Now simplify:

    12−xx2\frac{\frac{1}{2} - x}{x^{2}}

  4. Add the constant of integration:

    12−xx2+constant\frac{\frac{1}{2} - x}{x^{2}}+ \mathrm{constant}

The answer is:

12−xx2+constant\frac{\frac{1}{2} - x}{x^{2}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                       
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 | x - 1           1     1
 | ----- dx = C + ---- - -
 |    3              2   x
 |   x            2*x     
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∫x−1x3 dx=C−1x+12x2\int \frac{x - 1}{x^{3}}\, dx = C - \frac{1}{x} + \frac{1}{2 x^{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-500000000000500000000000
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] 
-9.15365037903492e+37
-9.15365037903492e+37
The graph
Integral of (x-1)/x^3 dx

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

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