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Identical expressions
x^ two -3x+2sinx
x squared minus 3x plus 2 sinus of x
x to the power of two minus 3x plus 2 sinus of x
x2-3x+2sinx
x²-3x+2sinx
x to the power of 2-3x+2sinx
x^2-3x+2sinxdx
Similar expressions
x^2-3x-2sinx
x^2+3x+2sinx

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

The solution

You have entered [src]

 pi                         
  /                         
 |                          
 |  / 2                 \   
 |  \x  - 3*x + 2*sin(x)/ dx
 |                          
/                           
0

$$\int\limits_{0}^{\pi} \left(\left(x^{2} - 3 x\right) + 2 \sin{\left(x \right)}\right)\, dx$$

Integral(x^2 - 3*x + 2*sin(x), (x, 0, pi))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 3 x\right)\, dx = - 3 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $- \frac{3 x^{2}}{2}$
  The result is: $\frac{x^{3}}{3} - \frac{3 x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \sin{\left(x \right)}\, dx = 2 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- 2 \cos{\left(x \right)}$
The result is: $\frac{x^{3}}{3} - \frac{3 x^{2}}{2} - 2 \cos{\left(x \right)}$
Add the constant of integration:

$\frac{x^{3}}{3} - \frac{3 x^{2}}{2} - 2 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{3}}{3} - \frac{3 x^{2}}{2} - 2 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                   
 |                                              2    3
 | / 2                 \                     3*x    x 
 | \x  - 3*x + 2*sin(x)/ dx = C - 2*cos(x) - ---- + --
 |                                            2     3 
/

$$\int \left(\left(x^{2} - 3 x\right) + 2 \sin{\left(x \right)}\right)\, dx = C + \frac{x^{3}}{3} - \frac{3 x^{2}}{2} - 2 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

        2     3
    3*pi    pi 
4 - ----- + ---
      2      3

$$- \frac{3 \pi^{2}}{2} + 4 + \frac{\pi^{3}}{3}$$

        2     3
    3*pi    pi 
4 - ----- + ---
      2      3

$$- \frac{3 \pi^{2}}{2} + 4 + \frac{\pi^{3}}{3}$$

4 - 3*pi^2/2 + pi^3/3

Numerical answer [src]

-0.468981041534098

-0.468981041534098

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

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

Limits of integration:

The graph:

Piecewise:

The solution