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3x^3+3x
Solving integrals/ 3x^3+3x

Integral of 3x^3+3x dx

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The solution

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∫01(3x3+3x) dx\int\limits_{0}^{1} \left(3 x^{3} + 3 x\right)\, dx 
Integral(3*x^3 + 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:

      ∫3x dx=3∫x dx\int 3 x\, dx = 3 \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: 3x22\frac{3 x^{2}}{2}

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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 | /   3      \          3*x    3*x 
 | \3*x  + 3*x/ dx = C + ---- + ----
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3 x44+3 x22{{3\,x^4}\over{4}}+{{3\,x^2}\over{2}}
Simplify
The graph
-2.0-1.5-1.0-0.54.00.00.51.01.52.02.53.03.5-250250
Plot the graph f(x)
The answer [src] 
9/4
94{{9}\over{4}} 
=
= 
9/4
94\frac{9}{4}
Упростить
Numerical answer [src] 
2.25
2.25
The graph
Integral of 3x^3+3x dx

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

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