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(4x^3+2x)
Solving integrals/ (4x^3+2x)

Integral of (4x^3+2x) dx

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The solution

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-2
∫−23(4x3+2x) dx\int\limits_{-2}^{3} \left(4 x^{3} + 2 x\right)\, dx 
Integral(4*x^3 + 2*x, (x, -2, 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:

      ∫4x3 dx=4∫x3 dx\int 4 x^{3}\, dx = 4 \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: x4x^{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: x4+x2x^{4} + x^{2}

  2. Add the constant of integration:

    x4+x2+constantx^{4} + x^{2}+ \mathrm{constant}

The answer is:

x4+x2+constantx^{4} + x^{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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 | /   3      \           2    4
 | \4*x  + 2*x/ dx = C + x  + x 
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x4+x2x^4+x^2
Simplify
The graph
-2.0-1.5-1.0-0.53.00.00.51.01.52.02.5-200200
Plot the graph f(x)
The answer [src] 
70
7070 
=
= 
70
7070
Simplify
Numerical answer [src] 
70.0
70.0
The graph
Integral of (4x^3+2x) dx

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

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