Mister Exam

Other calculators

Solving integrals/ (sinx+1/sin^2x)

Integral of (sinx+1/sin^2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    1. The integral of sine is negative cosine:

    1. Don't know the steps in finding this integral.

      But the integral is

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

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

    © Mister Exam – Calculator