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Identical expressions
tan^ two (x)sec^ two (x)
tangent of squared (x)sec squared (x)
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tan to the power of 2(x)sec to the power of 2(x)
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tan^2(x)sec^2(x)dx

Solving integrals/ tan^2(x)sec^2(x)

Integral of tan^2(x)sec^2(x) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |     2       2      
 |  tan (x)*sec (x) dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}\, dx$$

Integral(tan(x)^2*sec(x)^2, (x, 0, 1))

Detail solution

Let $u = \tan{\left(x \right)}$ .

Then let $du = \left(\tan^{2}{\left(x \right)} + 1\right) dx$ and substitute $du$ :

$\int u^{2}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{2}\, du = \frac{u^{3}}{3}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                
 |                             3   
 |    2       2             tan (x)
 | tan (x)*sec (x) dx = C + -------
 |                             3   
/

$$\int \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}\, dx = C + \frac{\tan^{3}{\left(x \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   sin(1)      sin(1) 
- -------- + ---------
  3*cos(1)        3   
             3*cos (1)

$$- \frac{\sin{\left(1 \right)}}{3 \cos{\left(1 \right)}} + \frac{\sin{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}}$$

   sin(1)      sin(1) 
- -------- + ---------
  3*cos(1)        3   
             3*cos (1)

$$- \frac{\sin{\left(1 \right)}}{3 \cos{\left(1 \right)}} + \frac{\sin{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}}$$

-sin(1)/(3*cos(1)) + sin(1)/(3*cos(1)^3)

Numerical answer [src]

1.25917391594425

1.25917391594425

The graph

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

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Identical expressions

Integral of tan^2(x)sec^2(x) dx

Limits of integration:

The graph:

Piecewise:

The solution