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Solving integrals/ cos(5x)+(1/x^2)

Integral of cos(5x)+(1/x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |  /           1 \   
 |  |cos(5*x) + --| dx
 |  |            2|   
 |  \           x /   
 |                    
/                     
0
$$\int\limits_{0}^{1} \left(\cos{\left(5 x \right)} + \frac{1}{x^{2}}\right)\, dx$$ 
Integral(cos(5*x) + 1/(x^2), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    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 cosine is sine:

        So, the result is:

      Now substitute back in:

      PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=0, context=1/(x**2), symbol=x), False), (ArccothRule(a=1, b=1, c=0, context=1/(x**2), symbol=x), False), (ArctanhRule(a=1, b=1, c=0, context=1/(x**2), symbol=x), False)], context=1/(x**2), symbol=x)

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                        
 |                         
 | /           1 \         
 | |cos(5*x) + --| dx = nan
 | |            2|         
 | \           x /         
 |                         
/
$$\int \left(\cos{\left(5 x \right)} + \frac{1}{x^{2}}\right)\, dx = \text{NaN}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo
$$\infty$$ 
=
= 
oo
$$\infty$$ 
oo
Numerical answer [src] 
1.3793236779486e+19
1.3793236779486e+19

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

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