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Integral of sec^2y/(tgy) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     2      
 |  sec (y)   
 |  ------- dy
 |   tan(y)   
 |            
/             
0             
$$\int\limits_{0}^{1} \frac{\sec^{2}{\left(y \right)}}{\tan{\left(y \right)}}\, dy$$
Integral(sec(y)^2/tan(y), (y, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. 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 is .

        So, the result is:

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            
 |                             
 |    2                        
 | sec (y)                     
 | ------- dy = C + log(tan(y))
 |  tan(y)                     
 |                             
/                              
$$\int \frac{\sec^{2}{\left(y \right)}}{\tan{\left(y \right)}}\, dy = C + \log{\left(\tan{\left(y \right)} \right)}$$
The graph
The answer [src]
     pi*I
oo - ----
      2  
$$\infty - \frac{i \pi}{2}$$
=
=
     pi*I
oo - ----
      2  
$$\infty - \frac{i \pi}{2}$$
oo - pi*i/2
Numerical answer [src]
44.5334688581098
44.5334688581098

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