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

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

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

The solution

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  1                         
  /                         
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 |  / 2                 \   
 |  \x  - 2*x + 3*sin(x)/ dx
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(x^{2} - 2 x + 3 \sin{\left(x \right)}\right)\, dx$$

Integral(x^2 - 2*x + 3*sin(x), (x, 0, 1))

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/3 - 3*cos(1)

$$\frac{7}{3} - 3 \cos{\left(1 \right)}$$

7/3 - 3*cos(1)

$$\frac{7}{3} - 3 \cos{\left(1 \right)}$$

Упростить

Numerical answer [src]

0.712426415728914

0.712426415728914

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution