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

Limits of integration:

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The graph:

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Piecewise:

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
  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:

        1. Let .

          Then let and substitute :

          1. The integral of a constant times a function is the constant times the integral of the function:

            1. The integral of sine is negative cosine:

            So, the result is:

          Now substitute back in:

        So, the result is:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is .

        So, the result is:

      The result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                       
 |                                                        
 | /3                 \                         2*cos(5*x)
 | |- - 2*sin(5*x) + 1| dx = C + x + 3*log(x) + ----------
 | \x                 /                             5     
 |                                                        
/                                                         
$$\int \left(\left(- 2 \sin{\left(5 x \right)} + \frac{3}{x}\right) + 1\right)\, dx = C + x + 3 \log{\left(x \right)} + \frac{2 \cos{\left(5 x \right)}}{5}$$
The graph
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.