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Identical expressions
((two /x^ five)-3cosx)
((2 divide by x to the power of 5) minus 3 co sinus of e of x)
((two divide by x to the power of five) minus 3 co sinus of e of x)
((2/x5)-3cosx)
2/x5-3cosx
((2/x⁵)-3cosx)
2/x^5-3cosx
((2 divide by x^5)-3cosx)
((2/x^5)-3cosx)dx
Similar expressions
((2/x^5)+3cosx)

Integral of ((2/x^5)-3cosx) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /2            \   
 |  |-- - 3*cos(x)| dx
 |  | 5           |   
 |  \x            /   
 |                    
/                     
0

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

Integral(2/x^5 - 3*cos(x), (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:
  
  $\int \left(- 3 \cos{\left(x \right)}\right)\, dx = - 3 \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $- 3 \sin{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2}{x^{5}}\, dx = 2 \int \frac{1}{x^{5}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{1}{4 x^{4}}$
  So, the result is: $- \frac{1}{2 x^{4}}$
The result is: $- 3 \sin{\left(x \right)} - \frac{1}{2 x^{4}}$
Add the constant of integration:

$- 3 \sin{\left(x \right)} - \frac{1}{2 x^{4}}+ \mathrm{constant}$

The answer is:

$- 3 \sin{\left(x \right)} - \frac{1}{2 x^{4}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                        
 |                                         
 | /2            \                      1  
 | |-- - 3*cos(x)| dx = C - 3*sin(x) - ----
 | | 5           |                        4
 | \x            /                     2*x 
 |                                         
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

1.45349812331627e+76

1.45349812331627e+76

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

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Integral of ((2/x^5)-3cosx) dx

Limits of integration:

The graph:

Piecewise:

The solution