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Identical expressions
2x^(- three)+3sin(x)
2x to the power of ( minus 3) plus 3 sinus of (x)
2x to the power of ( minus three) plus 3 sinus of (x)
2x(-3)+3sin(x)
2x-3+3sinx
2x^-3+3sinx
2x^(-3)+3sin(x)dx
Similar expressions
2x^(-3)-3sin(x)
2x^(3)+3sin(x)
2x^(-3)+3sinx

Solving integrals/ 2x^(-3)+3sin(x)

Integral of 2x^(-3)+3sin(x) dx

The solution

You have entered [src]

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

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

Simplify

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$-3\,\cos x-{{1}\over{x^2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

Simplify

Numerical answer [src]

1.83073007580698e+38

1.83073007580698e+38

The graph

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

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Integral of 2x^(-3)+3sin(x) dx

Limits of integration:

The graph:

Piecewise:

The solution