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Solving integrals/ 3*x³+4x

Integral of 3*x³+4x dx

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Piecewise:

The solution

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∫−12(3x3+4x) dx\int\limits_{-1}^{2} \left(3 x^{3} + 4 x\right)\, dx 
Integral(3*x^3 + 4*x, (x, -1, 2))
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:

      ∫4x dx=4∫x dx\int 4 x\, dx = 4 \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: 2x22 x^{2}

    The result is: 3x44+2x2\frac{3 x^{4}}{4} + 2 x^{2}

  2. Now simplify:

    x2(3x2+8)4\frac{x^{2} \left(3 x^{2} + 8\right)}{4}

  3. Add the constant of integration:

    x2(3x2+8)4+constant\frac{x^{2} \left(3 x^{2} + 8\right)}{4}+ \mathrm{constant}

The answer is:

x2(3x2+8)4+constant\frac{x^{2} \left(3 x^{2} + 8\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
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 | /   3      \             2   3*x 
 | \3*x  + 4*x/ dx = C + 2*x  + ----
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∫(3x3+4x) dx=C+3x44+2x2\int \left(3 x^{3} + 4 x\right)\, dx = C + \frac{3 x^{4}}{4} + 2 x^{2}
Simplify
The graph
-1.00-0.75-0.50-0.252.000.000.250.500.751.001.251.501.75-5050
Plot the graph f(x)
The answer [src] 
69/4
694\frac{69}{4} 
=
= 
69/4
694\frac{69}{4} 
69/4
Numerical answer [src] 
17.25
17.25

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

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