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Identical expressions
f³¹(two x- five)(x+2)dx
f³¹(2x minus 5)(x plus 2)dx
f³¹(two x minus five)(x plus 2)dx
f³¹2x-5x+2dx
Similar expressions
f³¹(2x+5)(x+2)dx
f³¹(2x-5)(x-2)dx

Integral of f³¹(2x-5)(x+2)dx dx

The solution

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  1                        
  /                        
 |                         
 |   3                     
 |  f *(2*x - 5)*(x + 2) dx
 |                         
/                          
0

$$\int\limits_{0}^{1} f^{3} \left(2 x - 5\right) \left(x + 2\right)\, dx$$

Integral((f^3*(2*x - 5))*(x + 2), (x, 0, 1))

Detail solution

Rewrite the integrand:

$f^{3} \left(2 x - 5\right) \left(x + 2\right) = 2 f^{3} x^{2} - f^{3} x - 10 f^{3}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 f^{3} x^{2}\, dx = 2 f^{3} \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $\frac{2 f^{3} x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- f^{3} x\right)\, dx = - f^{3} \int x\, dx$
  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: $- \frac{f^{3} x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(- 10 f^{3}\right)\, dx = - 10 f^{3} x$
The result is: $\frac{2 f^{3} x^{3}}{3} - \frac{f^{3} x^{2}}{2} - 10 f^{3} x$
Now simplify:

$\frac{f^{3} x \left(4 x^{2} - 3 x - 60\right)}{6}$
Add the constant of integration:

$\frac{f^{3} x \left(4 x^{2} - 3 x - 60\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{f^{3} x \left(4 x^{2} - 3 x - 60\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                       
 |                                          3  2      3  3
 |  3                                  3   f *x    2*f *x 
 | f *(2*x - 5)*(x + 2) dx = C - 10*x*f  - ----- + -------
 |                                           2        3   
/

$$\int f^{3} \left(2 x - 5\right) \left(x + 2\right)\, dx = C + \frac{2 f^{3} x^{3}}{3} - \frac{f^{3} x^{2}}{2} - 10 f^{3} x$$

Simplify

The answer [src]

     3
-59*f 
------
  6

$$- \frac{59 f^{3}}{6}$$

     3
-59*f 
------
  6

$$- \frac{59 f^{3}}{6}$$

-59*f^3/6

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

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Integral of f³¹(2x-5)(x+2)dx dx

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The solution