Mister Exam

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Identical expressions
12x^ five -3x^(- four)
12x to the power of 5 minus 3x to the power of ( minus 4)
12x to the power of five minus 3x to the power of ( minus four)
12x5-3x(-4)
12x5-3x-4
12x⁵-3x^(-4)
12x^5-3x^-4
12x^5-3x^(-4)dx
Similar expressions
12x^5+3x^(-4)
12x^5-3x^(4)

Integral of 12x^5-3x^(-4) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |  /    5   3 \   
 |  |12*x  - --| dx
 |  |         4|   
 |  \        x /   
 |                 
/                  
0

$$\int\limits_{0}^{1} \left(12 x^{5} - \frac{3}{x^{4}}\right)\, dx$$

Integral(12*x^5 - 3/x^4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 12 x^{5}\, dx = 12 \int x^{5}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{5}\, dx = \frac{x^{6}}{6}$
  So, the result is: $2 x^{6}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{3}{x^{4}}\right)\, dx = - 3 \int \frac{1}{x^{4}}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{x^{4}}\, dx = - \frac{1}{3 x^{3}}$
  So, the result is: $\frac{1}{x^{3}}$
The result is: $2 x^{6} + \frac{1}{x^{3}}$
Now simplify:

$\frac{2 x^{9} + 1}{x^{3}}$
Add the constant of integration:

$\frac{2 x^{9} + 1}{x^{3}}+ \mathrm{constant}$

The answer is:

$\frac{2 x^{9} + 1}{x^{3}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 | /    5   3 \          1       6
 | |12*x  - --| dx = C + -- + 2*x 
 | |         4|           3       
 | \        x /          x        
 |                                
/

$$\int \left(12 x^{5} - \frac{3}{x^{4}}\right)\, dx = C + 2 x^{6} + \frac{1}{x^{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Numerical answer [src]

-2.34429336733757e+57

-2.34429336733757e+57

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

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Integral of 12x^5-3x^(-4) dx

Limits of integration:

The graph:

Piecewise:

The solution