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x+x^2
Solving integrals/ x+x^2

Integral of x+x^2 dx

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The solution

You have entered [src] 
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∫01(x2+x) dx\int\limits_{0}^{1} \left(x^{2} + x\right)\, dx 
Integral(x + x^2, (x, 0, 1))
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:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    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}

    The result is: x33+x22\frac{x^{3}}{3} + \frac{x^{2}}{2}

  2. Now simplify:

    x2(2x+3)6\frac{x^{2} \left(2 x + 3\right)}{6}

  3. Add the constant of integration:

    x2(2x+3)6+constant\frac{x^{2} \left(2 x + 3\right)}{6}+ \mathrm{constant}

The answer is:

x2(2x+3)6+constant\frac{x^{2} \left(2 x + 3\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x2+x) dx=C+x33+x22\int \left(x^{2} + x\right)\, dx = C + \frac{x^{3}}{3} + \frac{x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
5/6
56\frac{5}{6} 
=
= 
5/6
56\frac{5}{6} 
5/6
Numerical answer [src] 
0.833333333333333
0.833333333333333
The graph
Integral of x+x^2 dx

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

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