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

Integral of x^2-2x+2 dx

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The solution

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∫21((x2−2x)+2) dx\int\limits_{2}^{1} \left(\left(x^{2} - 2 x\right) + 2\right)\, dx 
Integral(x^2 - 2*x + 2, (x, 2, 1))
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:

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

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

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

      ∫2 dx=2x\int 2\, dx = 2 x

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

  2. Now simplify:

    x(x2−3x+6)3\frac{x \left(x^{2} - 3 x + 6\right)}{3}

  3. Add the constant of integration:

    x(x2−3x+6)3+constant\frac{x \left(x^{2} - 3 x + 6\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−3x+6)3+constant\frac{x \left(x^{2} - 3 x + 6\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫((x2−2x)+2) dx=C+x33−x2+2x\int \left(\left(x^{2} - 2 x\right) + 2\right)\, dx = C + \frac{x^{3}}{3} - x^{2} + 2 x
Simplify
The graph
1.002.001.101.201.301.401.501.601.701.801.9004
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
The graph
Integral of x^2-2x+2 dx

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

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