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3x^5

Integral of 3x^5 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
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 |     5   
 |  3*x  dx
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013x5dx\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:

    3x5dx=3x5dx\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 n1n \neq -1:

      x5dx=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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3x5dx=C+x62\int 3 x^{5}\, dx = C + \frac{x^{6}}{2}
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
The answer [src]
1/2
12\frac{1}{2}
=
=
1/2
12\frac{1}{2}
1/2
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.