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Similar expressions
ctgx-1/sin^2(x)

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

The solution

You have entered [src]

  1                      
  /                      
 |                       
 |  /            1   \   
 |  |cot(x) + -------| dx
 |  |            2   |   
 |  \         sin (x)/   
 |                       
/                        
0

$$\int\limits_{0}^{1} \left(\cot{\left(x \right)} + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx$$

Integral(cot(x) + 1/(sin(x)^2), (x, 0, 1))

Detail solution

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

$\log{\left(\sin{\left(x \right)} \right)} - \frac{1}{\tan{\left(x \right)}}$
Add the constant of integration:

$\log{\left(\sin{\left(x \right)} \right)} - \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$\log{\left(\sin{\left(x \right)} \right)} - \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                                 
 | /            1   \          cos(x)              
 | |cot(x) + -------| dx = C - ------ + log(sin(x))
 | |            2   |          sin(x)              
 | \         sin (x)/                              
 |                                                 
/

$$\int \left(\cot{\left(x \right)} + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx = C + \log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

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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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution