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Solving integrals/ x^2-8*x+15

Integral of x^2-8*x+15 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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∫35((x2−8x)+15) dx\int\limits_{3}^{5} \left(\left(x^{2} - 8 x\right) + 15\right)\, dx 
Integral(x^2 - 8*x + 15, (x, 3, 5))
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:

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

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

        ∫(−8x) dx=−8∫x dx\int \left(- 8 x\right)\, dx = - 8 \int x\, dx

        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}

        So, the result is: −4x2- 4 x^{2}

      The result is: x33−4x2\frac{x^{3}}{3} - 4 x^{2}

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

      ∫15 dx=15x\int 15\, dx = 15 x

    The result is: x33−4x2+15x\frac{x^{3}}{3} - 4 x^{2} + 15 x

  2. Now simplify:

    x(x2−12x+45)3\frac{x \left(x^{2} - 12 x + 45\right)}{3}

  3. Add the constant of integration:

    x(x2−12x+45)3+constant\frac{x \left(x^{2} - 12 x + 45\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−12x+45)3+constant\frac{x \left(x^{2} - 12 x + 45\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  - 8*x + 15/ dx = C - 4*x  + 15*x + --
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∫((x2−8x)+15) dx=C+x33−4x2+15x\int \left(\left(x^{2} - 8 x\right) + 15\right)\, dx = C + \frac{x^{3}}{3} - 4 x^{2} + 15 x
Simplify
The graph
3.05.03.23.43.63.84.04.24.44.64.8-2020
Plot the graph f(x)
The answer [src] 
-4/3
−43- \frac{4}{3} 
=
= 
-4/3
−43- \frac{4}{3} 
-4/3
Numerical answer [src] 
-1.33333333333333
-1.33333333333333

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

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