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Identical expressions
one /secx+cscx
1 divide by secx plus cscx
one divide by secx plus cscx
1 divide by secx+cscx
1/secx+cscxdx
Similar expressions
1/secx-cscx

Integral of 1/secx+cscx dx

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |  /  1            \   
 |  |------ + csc(x)| dx
 |  \sec(x)         /   
 |                      
/                       
0

$$\int\limits_{0}^{1} \left(\csc{\left(x \right)} + \frac{1}{\sec{\left(x \right)}}\right)\, dx$$

Integral(1/sec(x) + csc(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Rewrite the integrand:
  
  $\csc{\left(x \right)} = \frac{\cot{\left(x \right)} \csc{\left(x \right)} + \csc^{2}{\left(x \right)}}{\cot{\left(x \right)} + \csc{\left(x \right)}}$
2. Let $u = \cot{\left(x \right)} + \csc{\left(x \right)}$ .
  
  Then let $du = \left(- \cot^{2}{\left(x \right)} - \cot{\left(x \right)} \csc{\left(x \right)} - 1\right) dx$ and substitute $- du$ :
  
  $\int \left(- \frac{1}{u}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{u}\, du = - \int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $- \log{\left(u \right)}$
  Now substitute $u$ back in:
  
  $- \log{\left(\cot{\left(x \right)} + \csc{\left(x \right)} \right)}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\sin{\left(x \right)}$
The result is: $- \log{\left(\cot{\left(x \right)} + \csc{\left(x \right)} \right)} + \sin{\left(x \right)}$
Add the constant of integration:

$- \log{\left(\cot{\left(x \right)} + \csc{\left(x \right)} \right)} + \sin{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- \log{\left(\cot{\left(x \right)} + \csc{\left(x \right)} \right)} + \sin{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                        
 |                                                         
 | /  1            \                                       
 | |------ + csc(x)| dx = C - log(cot(x) + csc(x)) + sin(x)
 | \sec(x)         /                                       
 |                                                         
/

$$\int \left(\csc{\left(x \right)} + \frac{1}{\sec{\left(x \right)}}\right)\, dx = C - \log{\left(\cot{\left(x \right)} + \csc{\left(x \right)} \right)} + \sin{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

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]

45.0204818534191

45.0204818534191

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

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Integral of 1/secx+cscx dx

Limits of integration:

The graph:

Piecewise:

The solution