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Identical expressions
(seven -3sin^2x)/(cos^2x)
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(seven minus 3 sinus of squared x) divide by ( co sinus of e of squared x)
(7-3sin2x)/(cos2x)
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(7-3sin^2x)/(cos^2x)dx
Similar expressions
(7+3sin^2x)/(cos^2x)

Solving integrals/ (7-3sin^2x)/(cos^2x)

Integral of (7-3sin^2x)/(cos^2x) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |           2      
 |  7 - 3*sin (x)   
 |  ------------- dx
 |        2         
 |     cos (x)      
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{7 - 3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}\, dx$$

Integral((7 - 3*sin(x)^2)/(cos(x)^2), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{7 - 3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} = - \frac{3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{7}{\cos^{2}{\left(x \right)}}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right)\, dx = - 3 \int \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
  So, the result is: $3 x - \frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{7}{\cos^{2}{\left(x \right)}}\, dx = 7 \int \frac{1}{\cos^{2}{\left(x \right)}}\, dx$
  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: $\frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)}}$
The result is: $3 x + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)}}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                     
 |                                      
 |          2                           
 | 7 - 3*sin (x)                4*sin(x)
 | ------------- dx = C + 3*x + --------
 |       2                       cos(x) 
 |    cos (x)                           
 |                                      
/

$$7\,\tan x-3\,\left(\tan x-x\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                                          2       
        3            8*tan(1/2)      3*tan (1/2)  
- -------------- - -------------- + --------------
          2                2                2     
  -1 + tan (1/2)   -1 + tan (1/2)   -1 + tan (1/2)

$$4\,\tan 1+3$$

                                          2       
        3            8*tan(1/2)      3*tan (1/2)  
- -------------- - -------------- + --------------
          2                2                2     
  -1 + tan (1/2)   -1 + tan (1/2)   -1 + tan (1/2)

$$\frac{3 \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{3}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{8 \tan{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}}$$

Упростить

Numerical answer [src]

9.22963089861961

9.22963089861961

The graph

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

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Integral of (7-3sin^2x)/(cos^2x) dx

Limits of integration:

The graph:

Piecewise:

The solution