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dx/cos^4x

Integral of dx/cos^4x dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |       1      
 |  1*------- dx
 |       4      
 |    cos (x)   
 |              
/               
0               
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{\cos^{4}{\left(x \right)}}\, dx$$
Integral(1/cos(x)^4, (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. Integrate term-by-term:

        1. The integral of is when :

        1. The integral of a constant is the constant times the variable of integration:

        The result is:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Let .

        Then let and substitute :

        1. The integral of is when :

        Now substitute back in:

      The result is:

    Method #3

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Let .

        Then let and substitute :

        1. The integral of is when :

        Now substitute back in:

      The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                   
 |                       3            
 |      1             tan (x)         
 | 1*------- dx = C + ------- + tan(x)
 |      4                3            
 |   cos (x)                          
 |                                    
/                                     
$${{\tan ^3x}\over{3}}+\tan x$$
The graph
The answer [src]
  sin(1)    2*sin(1)
--------- + --------
     3      3*cos(1)
3*cos (1)           
$${{\tan ^31}\over{3}}+\tan 1$$
=
=
  sin(1)    2*sin(1)
--------- + --------
     3      3*cos(1)
3*cos (1)           
$$\frac{2 \sin{\left(1 \right)}}{3 \cos{\left(1 \right)}} + \frac{\sin{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}}$$
Numerical answer [src]
2.81658164059915
2.81658164059915
The graph
Integral of dx/cos^4x dx

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