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Solving integrals/ 2x^3-3

Integral of 2x^3-3 dx

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The solution

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∫13(2x3−3) dx\int\limits_{1}^{3} \left(2 x^{3} - 3\right)\, dx 
Integral(2*x^3 - 3, (x, 1, 3))
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:

      ∫2x3 dx=2∫x3 dx\int 2 x^{3}\, dx = 2 \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: x42\frac{x^{4}}{2}

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

      ∫(−3) dx=−3x\int \left(-3\right)\, dx = - 3 x

    The result is: x42−3x\frac{x^{4}}{2} - 3 x

  2. Now simplify:

    x(x3−6)2\frac{x \left(x^{3} - 6\right)}{2}

  3. Add the constant of integration:

    x(x3−6)2+constant\frac{x \left(x^{3} - 6\right)}{2}+ \mathrm{constant}

The answer is:

x(x3−6)2+constant\frac{x \left(x^{3} - 6\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
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∫(2x3−3) dx=C+x42−3x\int \left(2 x^{3} - 3\right)\, dx = C + \frac{x^{4}}{2} - 3 x
Simplify
The graph
1.03.01.21.41.61.82.02.22.42.62.8-50100
Plot the graph f(x)
The answer [src] 
34
3434 
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34
3434 
34
Numerical answer [src] 
34.0
34.0

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

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