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

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

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
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∫01x2x+1 dx\int\limits_{0}^{1} \frac{x^{2}}{x + 1}\, dx 
Integral(x^2/(x + 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 \left(-1\right)\, 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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∫x2x+1 dx=C+x22−x+log⁡(x+1)\int \frac{x^{2}}{x + 1}\, dx = C + \frac{x^{2}}{2} - x + \log{\left(x + 1 \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
-1/2 + log(2)
−12+log⁡(2)- \frac{1}{2} + \log{\left(2 \right)} 
=
= 
-1/2 + log(2)
−12+log⁡(2)- \frac{1}{2} + \log{\left(2 \right)} 
-1/2 + log(2)
Numerical answer [src] 
0.193147180559945
0.193147180559945
The graph
Integral of (x^2)/(x+1) dx

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

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