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4x^3-x
Solving integrals/ 4x^3-x

Integral of 4x^3-x dx

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The solution

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-2
∫−21(4x3−x) dx\int\limits_{-2}^{1} \left(4 x^{3} - x\right)\, dx 
Integral(4*x^3 - x, (x, -2, 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:

      ∫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:

      ∫(−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: x4−x22x^{4} - \frac{x^{2}}{2}

  2. Add the constant of integration:

    x4−x22+constantx^{4} - \frac{x^{2}}{2}+ \mathrm{constant}

The answer is:

x4−x22+constantx^{4} - \frac{x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                           
 |                           2
 | /   3    \           4   x 
 | \4*x  - x/ dx = C + x  - --
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/
x4−x22x^4-{{x^2}\over{2}}
Simplify
The graph
-2.00-1.75-1.50-1.25-1.00-0.75-0.50-0.251.000.000.250.500.75-5050
Plot the graph f(x)
The answer [src] 
-27/2
−272-{{27}\over{2}} 
=
= 
-27/2
−272- \frac{27}{2}
Упростить
Numerical answer [src] 
-13.5
-13.5
The graph
Integral of 4x^3-x dx

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

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