Mister Exam

Other calculators


tag^5xsec^2xdx

Integral of tag^5xsec^2xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                     
  /                     
 |                      
 |     5       2        
 |  tan (x)*sec (x)*1 dx
 |                      
/                       
0                       
$$\int\limits_{0}^{1} \tan^{5}{\left(x \right)} \sec^{2}{\left(x \right)} 1\, dx$$
Integral(tan(x)^5*sec(x)^2*1, (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Let .

      Then let and substitute :

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

        1. The integral of is when :

        So, the result is:

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                  
 |                               6   
 |    5       2               tan (x)
 | tan (x)*sec (x)*1 dx = C + -------
 |                               6   
/                                    
$${{\tan ^6x}\over{6}}$$
The graph
The answer [src]
                4           2   
  1   -1 - 3*cos (1) + 3*cos (1)
- - - --------------------------
  6                6            
              6*cos (1)         
$$-{{1}\over{6\,\sin ^61-18\,\sin ^41+18\,\sin ^21-6}}-{{\sin ^41 }\over{2\,\sin ^61-6\,\sin ^41+6\,\sin ^21-2}}+{{\sin ^21}\over{2\, \sin ^61-6\,\sin ^41+6\,\sin ^21-2}}-{{1}\over{6}}$$
=
=
                4           2   
  1   -1 - 3*cos (1) + 3*cos (1)
- - - --------------------------
  6                6            
              6*cos (1)         
$$- \frac{1}{6} - \frac{-1 - 3 \cos^{4}{\left(1 \right)} + 3 \cos^{2}{\left(1 \right)}}{6 \cos^{6}{\left(1 \right)}}$$
Numerical answer [src]
2.37827842589157
2.37827842589157
The graph
Integral of tag^5xsec^2xdx dx

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