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x^ three +(one /x)-sinx
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Similar expressions
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Solving integrals/ x^3+(1/x)-sinx

Integral of x^3+(1/x)-sinx dx

The solution

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

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

Integral(x^3 + 1/x - sin(x), (x, 0, 0))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  The result is: $\frac{x^{4}}{4} + \log{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \sin{\left(x \right)}\right)\, dx = - \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $\cos{\left(x \right)}$
The result is: $\frac{x^{4}}{4} + \log{\left(x \right)} + \cos{\left(x \right)}$
Add the constant of integration:

$\frac{x^{4}}{4} + \log{\left(x \right)} + \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{4}}{4} + \log{\left(x \right)} + \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                             4                  
 | / 3   1         \          x                   
 | |x  + - - sin(x)| dx = C + -- + cos(x) + log(x)
 | \     x         /          4                   
 |                                                
/

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

Simplify

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Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

The graph

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

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Integral of x^3+(1/x)-sinx dx

Limits of integration:

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Piecewise:

The solution