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Solving integrals/ (7x²+3x³+4x^5)

Integral of (7x²+3x³+4x^5) dx

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The solution

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 |  /   2      3      5\   
 |  \7*x  + 3*x  + 4*x / dx
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∫01(4x5+(3x3+7x2)) dx\int\limits_{0}^{1} \left(4 x^{5} + \left(3 x^{3} + 7 x^{2}\right)\right)\, dx 
Integral(7*x^2 + 3*x^3 + 4*x^5, (x, 0, 1))
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:

      ∫4x5 dx=4∫x5 dx\int 4 x^{5}\, dx = 4 \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: 2x63\frac{2 x^{6}}{3}

    1. Integrate term-by-term:

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

        ∫3x3 dx=3∫x3 dx\int 3 x^{3}\, dx = 3 \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: 3x44\frac{3 x^{4}}{4}

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

        ∫7x2 dx=7∫x2 dx\int 7 x^{2}\, dx = 7 \int x^{2}\, dx

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

          ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

        So, the result is: 7x33\frac{7 x^{3}}{3}

      The result is: 3x44+7x33\frac{3 x^{4}}{4} + \frac{7 x^{3}}{3}

    The result is: 2x63+3x44+7x33\frac{2 x^{6}}{3} + \frac{3 x^{4}}{4} + \frac{7 x^{3}}{3}

  2. Now simplify:

    x3(8x3+9x+28)12\frac{x^{3} \left(8 x^{3} + 9 x + 28\right)}{12}

  3. Add the constant of integration:

    x3(8x3+9x+28)12+constant\frac{x^{3} \left(8 x^{3} + 9 x + 28\right)}{12}+ \mathrm{constant}

The answer is:

x3(8x3+9x+28)12+constant\frac{x^{3} \left(8 x^{3} + 9 x + 28\right)}{12}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                
 |                                  6      4      3
 | /   2      3      5\          2*x    3*x    7*x 
 | \7*x  + 3*x  + 4*x / dx = C + ---- + ---- + ----
 |                                3      4      3  
/
∫(4x5+(3x3+7x2)) dx=C+2x63+3x44+7x33\int \left(4 x^{5} + \left(3 x^{3} + 7 x^{2}\right)\right)\, dx = C + \frac{2 x^{6}}{3} + \frac{3 x^{4}}{4} + \frac{7 x^{3}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90020
Plot the graph f(x)
The answer [src] 
15/4
154\frac{15}{4} 
=
= 
15/4
154\frac{15}{4} 
15/4
Numerical answer [src] 
3.75
3.75

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

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