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Solving integrals/ 1/x-sin10x/x

Integral of 1/x-sin10x/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |  /1   sin(10*x)\   
 |  |- - ---------| dx
 |  \x       x    /   
 |                    
/                     
0
$$\int\limits_{0}^{1} \left(- \frac{\sin{\left(10 x \right)}}{x} + \frac{1}{x}\right)\, dx$$ 
Integral(1/x - sin(10*x)/x, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

        SiRule(a=10, b=0, context=sin(10*x)/x, symbol=x)

      So, the result is:

    1. The integral of is .

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                          
 |                                           
 | /1   sin(10*x)\                           
 | |- - ---------| dx = C - Si(10*x) + log(x)
 | \x       x    /                           
 |                                           
/
$$\int \left(- \frac{\sin{\left(10 x \right)}}{x} + \frac{1}{x}\right)\, dx = C + \log{\left(x \right)} - \operatorname{Si}{\left(10 x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo - Si(10)
$$- \operatorname{Si}{\left(10 \right)} + \infty$$ 
=
= 
oo - Si(10)
$$- \operatorname{Si}{\left(10 \right)} + \infty$$ 
oo - Si(10)
Numerical answer [src] 
42.432098539774
42.432098539774

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

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