Mister Exam

Other calculators

Solving integrals/ (1/x-sinx)dx

Integral of (1/x-sinx)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

      1. The integral of sine is negative cosine:

      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(x)| dx = C + cos(x) + log(x)
 | \x         /                         
 |                                      
/
$$\int \left(- \sin{\left(x \right)} + \frac{1}{x}\right)\, dx = C + \log{\left(x \right)} + \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo
$$\infty$$ 
=
= 
oo
$$\infty$$ 
oo
Numerical answer [src] 
43.630748439861
43.630748439861

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

    © Mister Exam – Calculator