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Identical expressions
(x+ six)x+67x!
(x plus 6)x plus 67x!
(x plus six)x plus 67x!
x+6x+67x!
(x+6)x+67x!dx
Similar expressions
(x+6)x-67x!
(x-6)x+67x!

Integral of (x+6)x+67x! dx

The solution

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  1                         
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 |  ((x + 6)*x + (67*x)!) dx
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0

$$\int\limits_{0}^{1} \left(x \left(x + 6\right) + \left(67 x\right)!\right)\, dx$$

Integral((x + 6)*x + factorial(67*x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Rewrite the integrand:
  
  $x \left(x + 6\right) = x^{2} + 6 x$
2. 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:
    
    $\int 6 x\, dx = 6 \int x\, dx$
    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: $3 x^{2}$
  The result is: $\frac{x^{3}}{3} + 3 x^{2}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \left(67 x\right)!\, dx$
The result is: $\frac{x^{3}}{3} + 3 x^{2} + \int \left(67 x\right)!\, dx$
Now simplify:

$\frac{x^{3}}{3} + 3 x^{2} + \int \Gamma\left(67 x + 1\right)\, dx$
Add the constant of integration:

$\frac{x^{3}}{3} + 3 x^{2} + \int \Gamma\left(67 x + 1\right)\, dx+ \mathrm{constant}$

The answer is:

$\frac{x^{3}}{3} + 3 x^{2} + \int \Gamma\left(67 x + 1\right)\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       3     /          
 |                                   2   x     |           
 | ((x + 6)*x + (67*x)!) dx = C + 3*x  + -- +  | (67*x)! dx
 |                                       3     |           
/                                             /

$$\int \left(x \left(x + 6\right) + \left(67 x\right)!\right)\, dx = C + \frac{x^{3}}{3} + 3 x^{2} + \int \left(67 x\right)!\, dx$$

Simplify

The answer [src]

  1                         
  /                         
 |                          
 |  (x*(6 + x) + (67*x)!) dx
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(x \left(x + 6\right) + \left(67 x\right)!\right)\, dx$$

  1                         
  /                         
 |                          
 |  (x*(6 + x) + (67*x)!) dx
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(x \left(x + 6\right) + \left(67 x\right)!\right)\, dx$$

Integral(x*(6 + x) + factorial(67*x), (x, 0, 1))

Numerical answer [src]

1.29341059922208e+92

1.29341059922208e+92

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

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Identical expressions

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Integral of (x+6)x+67x! dx

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The solution