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

You entered:

x^2/(x-1)

What you mean?

x^2/(x - 1*1)
 
x^2/x - 1*1
 
x*2/(x - 1*1)
 
x*2/x - 1*1
 
x^2/(x - 1*1)
 
x^2/x - 1*1
 
x^2/x - 1*1

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

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1         
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 |  x - 1   
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∫01x2x−1 dx\int\limits_{0}^{1} \frac{x^{2}}{x - 1}\, dx 
Integral(x^2/(x - 1*1), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    x2x−1=x+1+1x−1\frac{x^{2}}{x - 1} = x + 1 + \frac{1}{x - 1}

  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:

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

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

      ∫1 dx=x\int 1\, dx = x

    1. Let u=x−1u = x - 1.

      Then let du=dxdu = dx and substitute dudu:

      ∫1u du\int \frac{1}{u}\, du

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

      Now substitute uu back in:

      log⁡(x−1)\log{\left(x - 1 \right)}

    The result is: x22+x+log⁡(x−1)\frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}

  3. Add the constant of integration:

    x22+x+log⁡(x−1)+constant\frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}+ \mathrm{constant}

The answer is:

x22+x+log⁡(x−1)+constant\frac{x^{2}}{2} + x + \log{\left(x - 1 \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                   
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 |    2                2              
 |   x                x               
 | ----- dx = C + x + -- + log(-1 + x)
 | x - 1              2               
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x2+2 x2+log⁡(x−1){{x^2+2\,x}\over{2}}+\log \left(x-1\right)
Simplify
The answer [src] 
-oo - pi*I
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=
= 
-oo - pi*I
−∞−iπ-\infty - i \pi
Упростить
Numerical answer [src] 
-42.5909567862195
-42.5909567862195

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

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