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Solving integrals/ 3x^3-x

Integral of 3x^3-x dx

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The solution

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∫01(3x3−x) dx\int\limits_{0}^{1} \left(3 x^{3} - x\right)\, dx 
Integral(3*x^3 - x, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

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

      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}

      So, the result is: 3x44\frac{3 x^{4}}{4}

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

      ∫(−x) dx=−∫x dx\int \left(- x\right)\, dx = - \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: −x22- \frac{x^{2}}{2}

    The result is: 3x44−x22\frac{3 x^{4}}{4} - \frac{x^{2}}{2}

  2. Now simplify:

    x2(3x2−2)4\frac{x^{2} \left(3 x^{2} - 2\right)}{4}

  3. Add the constant of integration:

    x2(3x2−2)4+constant\frac{x^{2} \left(3 x^{2} - 2\right)}{4}+ \mathrm{constant}

The answer is:

x2(3x2−2)4+constant\frac{x^{2} \left(3 x^{2} - 2\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(3x3−x) dx=C+3x44−x22\int \left(3 x^{3} - x\right)\, dx = C + \frac{3 x^{4}}{4} - \frac{x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Plot the graph f(x)
The answer [src] 
1/4
14\frac{1}{4} 
=
= 
1/4
14\frac{1}{4} 
1/4
Numerical answer [src] 
0.25
0.25

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

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