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Solving integrals/ 3*x^2+3

Integral of 3*x^2+3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫01(3x2+3) dx\int\limits_{0}^{1} \left(3 x^{2} + 3\right)\, dx 
Integral(3*x^2 + 3, (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:

      ∫3x2 dx=3∫x2 dx\int 3 x^{2}\, dx = 3 \int x^{2}\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: x3x^{3}

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

      ∫3 dx=3x\int 3\, dx = 3 x

    The result is: x3+3xx^{3} + 3 x

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫(3x2+3) dx=C+x3+3x\int \left(3 x^{2} + 3\right)\, dx = C + x^{3} + 3 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
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    Use the examples entering the upper and lower limits of integration.

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