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Identical expressions
two *sin(x)+ five /x+ three
2 multiply by sinus of (x) plus 5 divide by x plus 3
two multiply by sinus of (x) plus five divide by x plus three
2sin(x)+5/x+3
2sinx+5/x+3
2*sin(x)+5 divide by x+3
2*sin(x)+5/x+3dx
Similar expressions
2*sin(x)+5/x-3
2*sin(x)-5/x+3
2*sinx+5/x+3

Integral of 2*sin(x)+5/x+3 dx

The solution

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

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

Integral(2*sin(x) + 5/x + 3, (x, 0, 1))

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

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]

224.371626058228

224.371626058228

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

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Integral of 2*sin(x)+5/x+3 dx

Limits of integration:

The graph:

Piecewise:

The solution