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Identical expressions
tan(x)(sec(x))^ three
tangent of (x)(sec(x)) cubed
tangent of (x)(sec(x)) to the power of three
tan(x)(sec(x))3
tanxsecx3
tan(x)(sec(x))³
tan(x)(sec(x)) to the power of 3
tanxsecx^3
tan(x)(sec(x))^3dx

Integral of tan(x)(sec(x))^3 dx

The solution

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  1                  
  /                  
 |                   
 |            3      
 |  tan(x)*sec (x) dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \tan{\left(x \right)} \sec^{3}{\left(x \right)}\, dx$$

Integral(tan(x)*sec(x)^3, (x, 0, 1))

Detail solution

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

Then let $du = \tan{\left(x \right)} \sec{\left(x \right)} dx$ 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:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

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

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

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

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

Numerical answer [src]

1.7800013582586

1.7800013582586

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

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Identical expressions

Integral of tan(x)(sec(x))^3 dx

Limits of integration:

The graph:

Piecewise:

The solution