Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sin(x)*dx/x
Integral of 1/sqrt(x^2+1)
Integral of x^3*ln(x)
Integral of x*ln(x+1)dx
Identical expressions
tan^ two (x/ two)
tangent of squared (x divide by 2)
tangent of to the power of two (x divide by two)
tan2(x/2)
tan2x/2
tan²(x/2)
tan to the power of 2(x/2)
tan^2x/2
tan^2(x divide by 2)
tan^2(x/2)dx

Solving integrals/ tan^2(x/2)

Integral of tan^2(x/2) dx

The solution

You have entered [src]

  1           
  /           
 |            
 |     2/x\   
 |  tan |-| dx
 |      \2/   
 |            
/             
0

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

Integral(tan(x/2)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

     2*sin(1/2)
-1 + ----------
      cos(1/2)

$$-1 + \frac{2 \sin{\left(\frac{1}{2} \right)}}{\cos{\left(\frac{1}{2} \right)}}$$

     2*sin(1/2)
-1 + ----------
      cos(1/2)

$$-1 + \frac{2 \sin{\left(\frac{1}{2} \right)}}{\cos{\left(\frac{1}{2} \right)}}$$

-1 + 2*sin(1/2)/cos(1/2)

Numerical answer [src]

0.092604979687581

0.092604979687581

The graph

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

Other calculators

How to use it?

Identical expressions

Integral of tan^2(x/2) dx

Limits of integration:

The graph:

Piecewise:

The solution