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  • Identical expressions

  • (2cos^3x+ five)/(cos^2x)
  • (2 co sinus of e of cubed x plus 5) divide by ( co sinus of e of squared x)
  • (2 co sinus of e of cubed x plus five) divide by ( co sinus of e of squared x)
  • (2cos3x+5)/(cos2x)
  • 2cos3x+5/cos2x
  • (2cos³x+5)/(cos²x)
  • (2cos to the power of 3x+5)/(cos to the power of 2x)
  • 2cos^3x+5/cos^2x
  • (2cos^3x+5) divide by (cos^2x)
  • (2cos^3x+5)/(cos^2x)dx

  • Similar expressions

  • (2cos^3x-5)/(cos^2x)
Solving integrals/ (2cos^3x+5)/(cos^2x)

Integral of (2cos^3x+5)/(cos^2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |       3          
 |  2*cos (x) + 5   
 |  ------------- dx
 |        2         
 |     cos (x)      
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{2 \cos^{3}{\left(x \right)} + 5}{\cos^{2}{\left(x \right)}}\, dx$$ 
Integral((2*cos(x)^3 + 5)/cos(x)^2, (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    The result is:

  3. Now simplify:

  4. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                          
 |                                           
 |      3                                    
 | 2*cos (x) + 5                     5*sin(x)
 | ------------- dx = C + 2*sin(x) + --------
 |       2                            cos(x) 
 |    cos (x)                                
 |                                           
/
$$\int \frac{2 \cos^{3}{\left(x \right)} + 5}{\cos^{2}{\left(x \right)}}\, dx = C + 2 \sin{\left(x \right)} + \frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                         3       
   14*tan(1/2)      6*tan (1/2)  
- -------------- - --------------
          4                4     
  -1 + tan (1/2)   -1 + tan (1/2)
$$- \frac{6 \tan^{3}{\left(\frac{1}{2} \right)}}{-1 + \tan^{4}{\left(\frac{1}{2} \right)}} - \frac{14 \tan{\left(\frac{1}{2} \right)}}{-1 + \tan^{4}{\left(\frac{1}{2} \right)}}$$ 
=
= 
                         3       
   14*tan(1/2)      6*tan (1/2)  
- -------------- - --------------
          4                4     
  -1 + tan (1/2)   -1 + tan (1/2)
$$- \frac{6 \tan^{3}{\left(\frac{1}{2} \right)}}{-1 + \tan^{4}{\left(\frac{1}{2} \right)}} - \frac{14 \tan{\left(\frac{1}{2} \right)}}{-1 + \tan^{4}{\left(\frac{1}{2} \right)}}$$ 
-14*tan(1/2)/(-1 + tan(1/2)^4) - 6*tan(1/2)^3/(-1 + tan(1/2)^4)
Numerical answer [src] 
9.4699805928903
9.4699805928903

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

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