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Solving integrals/ x^3-3x^2+5

Integral of x^3-3x^2+5 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫13((x3−3x2)+5) dx\int\limits_{1}^{3} \left(\left(x^{3} - 3 x^{2}\right) + 5\right)\, dx 
Integral(x^3 - 3*x^2 + 5, (x, 1, 3))
Detail solution

  1. Integrate term-by-term:

    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:

        ∫(−3x2) dx=−3∫x2 dx\int \left(- 3 x^{2}\right)\, dx = - 3 \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: −x3- x^{3}

      The result is: x44−x3\frac{x^{4}}{4} - x^{3}

    1. The integral of a constant is the constant times the variable of integration:

      ∫5 dx=5x\int 5\, dx = 5 x

    The result is: x44−x3+5x\frac{x^{4}}{4} - x^{3} + 5 x

  2. Now simplify:

    x(x34−x2+5)x \left(\frac{x^{3}}{4} - x^{2} + 5\right)

  3. Add the constant of integration:

    x(x34−x2+5)+constantx \left(\frac{x^{3}}{4} - x^{2} + 5\right)+ \mathrm{constant}

The answer is:

x(x34−x2+5)+constantx \left(\frac{x^{3}}{4} - x^{2} + 5\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | / 3      2    \           3         x 
 | \x  - 3*x  + 5/ dx = C - x  + 5*x + --
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∫((x3−3x2)+5) dx=C+x44−x3+5x\int \left(\left(x^{3} - 3 x^{2}\right) + 5\right)\, dx = C + \frac{x^{4}}{4} - x^{3} + 5 x
Simplify
The graph
1.03.01.21.41.61.82.02.22.42.62.8010
Plot the graph f(x)
The answer [src] 
4
44 
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4
44 
4
Numerical answer [src] 
4.0
4.0

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

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