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Integral of d{x}:
Integral of e^(-x)
Integral of -sin(x)
Integral of cos(x/2)
Integral of x-2
Identical expressions
((x)^ two +(two)^x-3cosx+ one /2sinx- one /x)*dx
((x) squared plus (2) to the power of x minus 3 co sinus of e of x plus 1 divide by 2 sinus of x minus 1 divide by x) multiply by dx
((x) to the power of two plus (two) to the power of x minus 3 co sinus of e of x plus one divide by 2 sinus of x minus one divide by x) multiply by dx
((x)2+(2)x-3cosx+1/2sinx-1/x)*dx
x2+2x-3cosx+1/2sinx-1/x*dx
((x)²+(2)^x-3cosx+1/2sinx-1/x)*dx
((x) to the power of 2+(2) to the power of x-3cosx+1/2sinx-1/x)*dx
((x)^2+(2)^x-3cosx+1/2sinx-1/x)dx
((x)2+(2)x-3cosx+1/2sinx-1/x)dx
x2+2x-3cosx+1/2sinx-1/xdx
x^2+2^x-3cosx+1/2sinx-1/xdx
((x)^2+(2)^x-3cosx+1 divide by 2sinx-1 divide by x)*dx
Similar expressions
((x)^2+(2)^x-3cosx+1/2sinx+1/x)*dx
((x)^2-(2)^x-3cosx+1/2sinx-1/x)*dx
((x)^2+(2)^x+3cosx+1/2sinx-1/x)*dx
((x)^2+(2)^x-3cosx-1/2sinx-1/x)*dx

Solving integrals/ ((x)^2+(2)^x-3cosx+1/2sinx-1/x)*dx

Integral of ((x)^2+(2)^x-3cosx+1/2sinx-1/x)*dx dx

The solution

You have entered [src]

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

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

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

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

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0.0

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

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Identical expressions

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Integral of ((x)^2+(2)^x-3cosx+1/2sinx-1/x)*dx dx

Limits of integration:

The graph:

Piecewise:

The solution