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7x^3+4x^2
Solving integrals/ 7x^3+4x^2

Integral of 7x^3+4x^2 dx

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The solution

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

      ∫7x3 dx=7∫x3 dx\int 7 x^{3}\, dx = 7 \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: 7x44\frac{7 x^{4}}{4}

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

      ∫4x2 dx=4∫x2 dx\int 4 x^{2}\, dx = 4 \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: 4x33\frac{4 x^{3}}{3}

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

  2. Now simplify:

    x3⋅(21x+16)12\frac{x^{3} \cdot \left(21 x + 16\right)}{12}

  3. Add the constant of integration:

    x3⋅(21x+16)12+constant\frac{x^{3} \cdot \left(21 x + 16\right)}{12}+ \mathrm{constant}

The answer is:

x3⋅(21x+16)12+constant\frac{x^{3} \cdot \left(21 x + 16\right)}{12}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                           3      4
 | /   3      2\          4*x    7*x 
 | \7*x  + 4*x / dx = C + ---- + ----
 |                         3      4  
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7 x44+4 x33{{7\,x^4}\over{4}}+{{4\,x^3}\over{3}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90020
Plot the graph f(x)
The answer [src] 
37
--
12
3712{{37}\over{12}} 
=
= 
37
--
12
3712\frac{37}{12}
Simplify
Numerical answer [src] 
3.08333333333333
3.08333333333333
The graph
Integral of 7x^3+4x^2 dx

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

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