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(x^3+2x^2+x)
Solving integrals/ (x^3+2x^2+x)

Integral of (x^3+2x^2+x) dx

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The solution

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0
∫01(x3+2x2+x) dx\int\limits_{0}^{1} \left(x^{3} + 2 x^{2} + x\right)\, dx 
Integral(x^3 + 2*x^2 + x, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    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}

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

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

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

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    The result is: x44+2x33+x22\frac{x^{4}}{4} + \frac{2 x^{3}}{3} + \frac{x^{2}}{2}

  2. Now simplify:

    x2⋅(3x2+8x+6)12\frac{x^{2} \cdot \left(3 x^{2} + 8 x + 6\right)}{12}

  3. Add the constant of integration:

    x2⋅(3x2+8x+6)12+constant\frac{x^{2} \cdot \left(3 x^{2} + 8 x + 6\right)}{12}+ \mathrm{constant}

The answer is:

x2⋅(3x2+8x+6)12+constant\frac{x^{2} \cdot \left(3 x^{2} + 8 x + 6\right)}{12}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                       
 |                           2    4      3
 | / 3      2    \          x    x    2*x 
 | \x  + 2*x  + x/ dx = C + -- + -- + ----
 |                          2    4     3  
/
x44+2 x33+x22{{x^4}\over{4}}+{{2\,x^3}\over{3}}+{{x^2}\over{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
17
--
12
1712{{17}\over{12}} 
=
= 
17
--
12
1712\frac{17}{12}
Simplify
Numerical answer [src] 
1.41666666666667
1.41666666666667
The graph
Integral of (x^3+2x^2+x) dx

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

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