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x^3+8
Solving integrals/ x^3+8

Integral of x^3+8 dx

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The solution

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∫01(x3+8) dx\int\limits_{0}^{1} \left(x^{3} + 8\right)\, dx 
Integral(x^3 + 8, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    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}

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

      ∫8 dx=8x\int 8\, dx = 8 x

    The result is: x44+8x\frac{x^{4}}{4} + 8 x

  2. Now simplify:

    x(x3+32)4\frac{x \left(x^{3} + 32\right)}{4}

  3. Add the constant of integration:

    x(x3+32)4+constant\frac{x \left(x^{3} + 32\right)}{4}+ \mathrm{constant}

The answer is:

x(x3+32)4+constant\frac{x \left(x^{3} + 32\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x3+8) dx=C+x44+8x\int \left(x^{3} + 8\right)\, dx = C + \frac{x^{4}}{4} + 8 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
33/4
334\frac{33}{4} 
=
= 
33/4
334\frac{33}{4} 
33/4
Numerical answer [src] 
8.25
8.25
The graph
Integral of x^3+8 dx

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

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