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Identical expressions
(four -tg^2x)/sin^2x
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Similar expressions
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Solving integrals/ (4-tg^2x)/sin^2x

Integral of (4-tg^2x)/sin^2x dx

The solution

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  1               
  /               
 |                
 |         2      
 |  4 - tan (x)   
 |  ----------- dx
 |       2        
 |    sin (x)     
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{- \tan^{2}{\left(x \right)} + 4}{\sin^{2}{\left(x \right)}}\, dx$$

Integral((4 - tan(x)^2)/(sin(x)^2), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{4 - \tan^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} = - \frac{\tan^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{4}{\sin^{2}{\left(x \right)}}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{\tan^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right)\, dx = - \int \frac{\tan^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
  So, the result is: $- \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{4}{\sin^{2}{\left(x \right)}}\, dx = 4 \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  So, the result is: $- \frac{4 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $- \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$- \tan{\left(x \right)} - \frac{4}{\tan{\left(x \right)}}$
Add the constant of integration:

$- \tan{\left(x \right)} - \frac{4}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- \tan{\left(x \right)} - \frac{4}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                      
 |                                       
 |        2                              
 | 4 - tan (x)          sin(x)   4*cos(x)
 | ----------- dx = C - ------ - --------
 |      2               cos(x)    sin(x) 
 |   sin (x)                             
 |                                       
/

$$-\tan x-{{4}\over{\tan x}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$${\it \%a}$$

oo

$$\infty$$

Simplify

Numerical answer [src]

5.51729471179439e+19

5.51729471179439e+19

The graph

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

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Integral of (4-tg^2x)/sin^2x dx

Limits of integration:

The graph:

Piecewise:

The solution