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Integral of d{x}:
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Integral of sin(x)^4
Integral of cos(x)^3
Integral of (e^(x^2))
Identical expressions
(two x^ four)/ three -3sinx-2/x+ four
(2x to the power of 4) divide by 3 minus 3 sinus of x minus 2 divide by x plus 4
(two x to the power of four) divide by three minus 3 sinus of x minus 2 divide by x plus four
(2x4)/3-3sinx-2/x+4
2x4/3-3sinx-2/x+4
(2x⁴)/3-3sinx-2/x+4
2x^4/3-3sinx-2/x+4
(2x^4) divide by 3-3sinx-2 divide by x+4
(2x^4)/3-3sinx-2/x+4dx
Similar expressions
(2x^4)/3-3sinx+2/x+4
(2x^4)/3+3sinx-2/x+4
(2x^4)/3-3sinx-2/x-4

Integral of (2x^4)/3-3sinx-2/x+4 dx

The solution

You have entered [src]

  1                             
  /                             
 |                              
 |  /   4                   \   
 |  |2*x               2    |   
 |  |---- - 3*sin(x) - - + 4| dx
 |  \ 3                x    /   
 |                              
/                               
0

$$\int\limits_{0}^{1} \left(\left(\left(\frac{2 x^{4}}{3} - 3 \sin{\left(x \right)}\right) - \frac{2}{x}\right) + 4\right)\, dx$$

Integral((2*x^4)/3 - 3*sin(x) - 2/x + 4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. Integrate term-by-term:
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{2 x^{4}}{3}\, dx = \frac{\int 2 x^{4}\, dx}{3}$
      1. The integral of a constant times a function is the constant times the integral of the function:
        
        $\int 2 x^{4}\, dx = 2 \int x^{4}\, dx$
        
        The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x^{4}\, dx = \frac{x^{5}}{5}$
        
        So, the result is: $\frac{2 x^{5}}{5}$
      So, the result is: $\frac{2 x^{5}}{15}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- 3 \sin{\left(x \right)}\right)\, dx = - 3 \int \sin{\left(x \right)}\, dx$
      1. The integral of sine is negative cosine:
        
        $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
      So, the result is: $3 \cos{\left(x \right)}$
    The result is: $\frac{2 x^{5}}{15} + 3 \cos{\left(x \right)}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{2}{x}\right)\, dx = - 2 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $- 2 \log{\left(x \right)}$
  The result is: $\frac{2 x^{5}}{15} - 2 \log{\left(x \right)} + 3 \cos{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
The result is: $\frac{2 x^{5}}{15} + 4 x - 2 \log{\left(x \right)} + 3 \cos{\left(x \right)}$
Add the constant of integration:

$\frac{2 x^{5}}{15} + 4 x - 2 \log{\left(x \right)} + 3 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{2 x^{5}}{15} + 4 x - 2 \log{\left(x \right)} + 3 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                   
 |                                                                    
 | /   4                   \                                         5
 | |2*x               2    |                                      2*x 
 | |---- - 3*sin(x) - - + 4| dx = C - 2*log(x) + 3*cos(x) + 4*x + ----
 | \ 3                x    /                                       15 
 |                                                                    
/

$$\int \left(\left(\left(\frac{2 x^{4}}{3} - 3 \sin{\left(x \right)}\right) - \frac{2}{x}\right) + 4\right)\, dx = C + \frac{2 x^{5}}{15} + 4 x - 2 \log{\left(x \right)} + 3 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$-\infty$$

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$$-\infty$$

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Numerical answer [src]

-85.426652017048

-85.426652017048

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

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Identical expressions

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Integral of (2x^4)/3-3sinx-2/x+4 dx

Limits of integration:

The graph:

Piecewise:

The solution