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Derivative of:
tg^2(2x)
Identical expressions
tg^ two (2x)
tg squared (2x)
tg to the power of two (2x)
tg2(2x)
tg22x
tg²(2x)
tg to the power of 2(2x)
tg^22x
tg^2(2x)dx

Solving integrals/ tg^2(2x)

Integral of tg^2(2x) dx

The solution

You have entered [src]

 pi             
 --             
 8              
  /             
 |              
 |     2        
 |  tan (2*x) dx
 |              
/               
0

$$\int\limits_{0}^{\frac{\pi}{8}} \tan^{2}{\left(2 x \right)}\, dx$$

Integral(tan(2*x)^2, (x, 0, pi/8))

Detail solution

Rewrite the integrand:

$\tan^{2}{\left(2 x \right)} = \sec^{2}{\left(2 x \right)} - 1$
Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\sin{\left(2 x \right)}}{2 \cos{\left(2 x \right)}}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $- x + \frac{\sin{\left(2 x \right)}}{2 \cos{\left(2 x \right)}}$
Now simplify:

$- x + \frac{\tan{\left(2 x \right)}}{2}$
Add the constant of integration:

$- x + \frac{\tan{\left(2 x \right)}}{2}+ \mathrm{constant}$

The answer is:

$- x + \frac{\tan{\left(2 x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                                  
 |    2                    sin(2*x) 
 | tan (2*x) dx = C - x + ----------
 |                        2*cos(2*x)
/

$$\int \tan^{2}{\left(2 x \right)}\, dx = C - x + \frac{\sin{\left(2 x \right)}}{2 \cos{\left(2 x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1   pi
- - --
2   8

$$\frac{1}{2} - \frac{\pi}{8}$$

1   pi
- - --
2   8

$$\frac{1}{2} - \frac{\pi}{8}$$

1/2 - pi/8

Numerical answer [src]

0.107300918301276

0.107300918301276

The graph

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

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Identical expressions

Integral of tg^2(2x) dx

Limits of integration:

The graph:

Piecewise:

The solution