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Identical expressions
(three /x)- two *sin(five *x)+ one
(3 divide by x) minus 2 multiply by sinus of (5 multiply by x) plus 1
(three divide by x) minus two multiply by sinus of (five multiply by x) plus one
(3/x)-2sin(5x)+1
3/x-2sin5x+1
(3 divide by x)-2*sin(5*x)+1
(3/x)-2*sin(5*x)+1dx
Similar expressions
(3/x)-2*sin(5*x)-1
(3/x)+2*sin(5*x)+1

Integral of (3/x)-2sin(5x)+1 dx

The solution

You have entered [src]

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

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

Integral(3/x - 2*sin(5*x) + 1, (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:
    
    $\int \left(- 2 \sin{\left(5 x \right)}\right)\, dx = - 2 \int \sin{\left(5 x \right)}\, dx$
    1. Let $u = 5 x$ .
      
      Then let $du = 5 dx$ and substitute $\frac{du}{5}$ :
      
      $\int \frac{\sin{\left(u \right)}}{5}\, du$
      1. The integral of a constant times a function is the constant times the integral of the function:
        
        $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{5}$
        
        The integral of sine is negative cosine:
        
        $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
        
        So, the result is: $- \frac{\cos{\left(u \right)}}{5}$
      Now substitute $u$ back in:
      
      $- \frac{\cos{\left(5 x \right)}}{5}$
    So, the result is: $\frac{2 \cos{\left(5 x \right)}}{5}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{3}{x}\, dx = 3 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $3 \log{\left(x \right)}$
  The result is: $3 \log{\left(x \right)} + \frac{2 \cos{\left(5 x \right)}}{5}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $x + 3 \log{\left(x \right)} + \frac{2 \cos{\left(5 x \right)}}{5}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                                       
 |                                                        
 | /3                 \                         2*cos(5*x)
 | |- - 2*sin(5*x) + 1| dx = C + x + 3*log(x) + ----------
 | \x                 /                             5     
 |                                                        
/

$$\int \left(\left(- 2 \sin{\left(5 x \right)} + \frac{3}{x}\right) + 1\right)\, dx = C + x + 3 \log{\left(x \right)} + \frac{2 \cos{\left(5 x \right)}}{5}$$

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]

132.984803276164

132.984803276164

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

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Identical expressions

Similar expressions

Integral of (3/x)-2sin(5x)+1 dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (3/x)-2*sin(5*x)+1 dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of (3/x)-2sin(5x)+1 dx