Mister Exam

Other calculators

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

Integral of x^2-2x+3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2                  
  /                  
 |                   
 |  / 2          \   
 |  \x  - 2*x + 3/ dx
 |                   
/                    
1
∫12((x2−2x)+3) dx\int\limits_{1}^{2} \left(\left(x^{2} - 2 x\right) + 3\right)\, dx 
Integral(x^2 - 2*x + 3, (x, 1, 2))
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:

      ∫3 dx=3x\int 3\, dx = 3 x

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                                     
 |                                     3
 | / 2          \           2         x 
 | \x  - 2*x + 3/ dx = C - x  + 3*x + --
 |                                    3 
/
∫((x2−2x)+3) dx=C+x33−x2+3x\int \left(\left(x^{2} - 2 x\right) + 3\right)\, dx = C + \frac{x^{3}}{3} - x^{2} + 3 x
Simplify
The graph
1.002.001.101.201.301.401.501.601.701.801.900.05.0
Plot the graph f(x)
The answer [src] 
7/3
73\frac{7}{3} 
=
= 
7/3
73\frac{7}{3} 
7/3
Numerical answer [src] 
2.33333333333333
2.33333333333333
The graph
Integral of x^2-2x+3 dx

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

    © Mister Exam – Calculator