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3x^5
Solving integrals/ 3x^5

Integral of 3x^5 dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
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 |     5   
 |  3*x  dx
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∫013x5 dx\int\limits_{0}^{1} 3 x^{5}\, dx 
Integral(3*x^5, (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫3x5 dx=3∫x5 dx\int 3 x^{5}\, dx = 3 \int x^{5}\, dx

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

      ∫x5 dx=x66\int x^{5}\, dx = \frac{x^{6}}{6}

    So, the result is: x62\frac{x^{6}}{2}

  2. Add the constant of integration:

    x62+constant\frac{x^{6}}{2}+ \mathrm{constant}

The answer is:

x62+constant\frac{x^{6}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                
 |                6
 |    5          x 
 | 3*x  dx = C + --
 |               2 
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∫3x5 dx=C+x62\int 3 x^{5}\, dx = C + \frac{x^{6}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
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12\frac{1}{2} 
=
= 
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12\frac{1}{2} 
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Numerical answer [src] 
0.5
0.5
The graph
Integral of 3x^5 dx

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

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