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x^2-6x+5
Solving integrals/ x^2-6x+5

Integral of x^2-6x+5 dx

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The solution

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∫01(x2−6x+5) dx\int\limits_{0}^{1} \left(x^{2} - 6 x + 5\right)\, dx 
Integral(x^2 - 6*x + 5, (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:

      ∫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:

      ∫(−6x) dx=−∫6x dx\int \left(- 6 x\right)\, dx = - \int 6 x\, dx

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

        ∫6x dx=6∫x dx\int 6 x\, dx = 6 \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: 3x23 x^{2}

      So, the result is: −3x2- 3 x^{2}

    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: x33−3x2+5x\frac{x^{3}}{3} - 3 x^{2} + 5 x

  2. Now simplify:

    x(x2−9x+15)3\frac{x \left(x^{2} - 9 x + 15\right)}{3}

  3. Add the constant of integration:

    x(x2−9x+15)3+constant\frac{x \left(x^{2} - 9 x + 15\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−9x+15)3+constant\frac{x \left(x^{2} - 9 x + 15\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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x33−3 x2+5 x{{x^3}\over{3}}-3\,x^2+5\,x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
7/3
73{{7}\over{3}} 
=
= 
7/3
73\frac{7}{3}
Simplify
Numerical answer [src] 
2.33333333333333
2.33333333333333
The graph
Integral of x^2-6x+5 dx

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

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