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(8x^3+1)
Solving integrals/ (8x^3+1)

Integral of (8x^3+1) dx

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The solution

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∫012(8x3+1) dx\int\limits_{0}^{\frac{1}{2}} \left(8 x^{3} + 1\right)\, dx 
Integral(8*x^3 + 1, (x, 0, 1/2))
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:

      ∫8x3 dx=8∫x3 dx\int 8 x^{3}\, dx = 8 \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: 2x42 x^{4}

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

      ∫1 dx=x\int 1\, dx = x

    The result is: 2x4+x2 x^{4} + x

  2. Add the constant of integration:

    2x4+x+constant2 x^{4} + x+ \mathrm{constant}

The answer is:

2x4+x+constant2 x^{4} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(8x3+1) dx=C+2x4+x\int \left(8 x^{3} + 1\right)\, dx = C + 2 x^{4} + x
Simplify
The graph
0.000.500.050.100.150.200.250.300.350.400.4504
Plot the graph f(x)
The answer [src] 
5/8
58\frac{5}{8} 
=
= 
5/8
58\frac{5}{8}
Упростить
Numerical answer [src] 
0.625
0.625
The graph
Integral of (8x^3+1) dx

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

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