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x^3+2
Solving integrals/ x^3+2

Integral of x^3+2 dx

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The solution

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∫01(x3+2) dx\int\limits_{0}^{1} \left(x^{3} + 2\right)\, dx 
Integral(x^3 + 2, (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:

      ∫2 dx=2x\int 2\, dx = 2 x

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

  2. Now simplify:

    x(x3+8)4\frac{x \left(x^{3} + 8\right)}{4}

  3. Add the constant of integration:

    x(x3+8)4+constant\frac{x \left(x^{3} + 8\right)}{4}+ \mathrm{constant}

The answer is:

x(x3+8)4+constant\frac{x \left(x^{3} + 8\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x3+2) dx=C+x44+2x\int \left(x^{3} + 2\right)\, dx = C + \frac{x^{4}}{4} + 2 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
9/4
94\frac{9}{4} 
=
= 
9/4
94\frac{9}{4} 
9/4
Numerical answer [src] 
2.25
2.25
The graph
Integral of x^3+2 dx

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

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