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Solving integrals/ 4-5sinxdx/cos^2x

Integral of 4-5sinxdx/cos^2x dx

The solution

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  0                            
  /                            
 |                             
 |  /                  1   \   
 |  |4 - 5*sin(x)*1*-------| dx
 |  |                  2   |   
 |  \               cos (x)/   
 |                             
/                              
0

$$\int\limits_{0}^{0} \left(- \frac{1 \cdot 5 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 4\right)\, dx$$

Integral(4 - 5*sin(x)/(cos(x)^2), (x, 0, 0))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1 \cdot 5 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right)\, dx = - \int \frac{5 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{5 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\, dx = 5 \int \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $\frac{1}{\cos{\left(x \right)}}$
    So, the result is: $\frac{5}{\cos{\left(x \right)}}$
  So, the result is: $- \frac{5}{\cos{\left(x \right)}}$
The result is: $4 x - \frac{5}{\cos{\left(x \right)}}$
Add the constant of integration:

$4 x - \frac{5}{\cos{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$4 x - \frac{5}{\cos{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 | /                  1   \            5         
 | |4 - 5*sin(x)*1*-------| dx = C - ------ + 4*x
 | |                  2   |          cos(x)      
 | \               cos (x)/                      
 |                                               
/

$$4\,x-{{5}\over{\cos x}}$$

Simplify

The graph

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The answer [src]

$$0$$

Simplify

Numerical answer [src]

0.0

0.0

The graph

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

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Integral of 4-5sinxdx/cos^2x dx

Limits of integration:

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Piecewise:

The solution