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Identical expressions
3tg^2x+ four /(sin^2x)
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Similar expressions
3tg^2x-4/(sin^2x)

Integral of 3tg^2x+4/(sin^2x) dx

The solution

You have entered [src]

  1                         
  /                         
 |                          
 |  /     2         4   \   
 |  |3*tan (x) + -------| dx
 |  |               2   |   
 |  \            sin (x)/   
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(3 \tan^{2}{\left(x \right)} + \frac{4}{\sin^{2}{\left(x \right)}}\right)\, dx$$

Integral(3*tan(x)^2 + 4/sin(x)^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 \tan^{2}{\left(x \right)}\, dx = 3 \int \tan^{2}{\left(x \right)}\, dx$
  1. Rewrite the integrand:
    
    $\tan^{2}{\left(x \right)} = \sec^{2}{\left(x \right)} - 1$
  2. Integrate term-by-term:
    1. $\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int \left(-1\right)\, dx = - x$
    The result is: $- x + \tan{\left(x \right)}$
  So, the result is: $- 3 x + 3 \tan{\left(x \right)}$
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: $- 3 x + 3 \tan{\left(x \right)} - \frac{4 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$- 3 x + 3 \tan{\left(x \right)} - \frac{4}{\tan{\left(x \right)}}$
Add the constant of integration:

$- 3 x + 3 \tan{\left(x \right)} - \frac{4}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- 3 x + 3 \tan{\left(x \right)} - \frac{4}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                        
 |                                                         
 | /     2         4   \                           4*cos(x)
 | |3*tan (x) + -------| dx = C - 3*x + 3*tan(x) - --------
 | |               2   |                            sin(x) 
 | \            sin (x)/                                   
 |                                                         
/

$$\int \left(3 \tan^{2}{\left(x \right)} + \frac{4}{\sin^{2}{\left(x \right)}}\right)\, dx = C - 3 x + 3 \tan{\left(x \right)} - \frac{4 \cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

5.51729471179439e+19

5.51729471179439e+19

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

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Similar expressions

Integral of 3tg^2x+4/(sin^2x) dx

Limits of integration:

The graph:

Piecewise:

The solution