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Solving integrals/ (x³+2x)

Integral of (x³+2x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫−13(x3+2x) dx\int\limits_{-1}^{3} \left(x^{3} + 2 x\right)\, dx 
Integral(x^3 + 2*x, (x, -1, 3))
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:

      ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

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

      ∫2x dx=2∫x dx\int 2 x\, dx = 2 \int x\, dx

      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}

      So, the result is: x2x^{2}

    The result is: x44+x2\frac{x^{4}}{4} + x^{2}

  2. Add the constant of integration:

    x44+x2+constant\frac{x^{4}}{4} + x^{2}+ \mathrm{constant}

The answer is:

x44+x2+constant\frac{x^{4}}{4} + x^{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                           
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∫(x3+2x) dx=C+x44+x2\int \left(x^{3} + 2 x\right)\, dx = C + \frac{x^{4}}{4} + x^{2}
Simplify
The graph
-1.0-0.53.00.00.51.01.52.02.5-5050
Plot the graph f(x)
The answer [src] 
28
2828 
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28
2828 
28
Numerical answer [src] 
28.0
28.0

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

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