Mister Exam

Integral of tg²xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     2      
 |  tan (x) dx
 |            
/             
0             
01tan2(x)dx\int\limits_{0}^{1} \tan^{2}{\left(x \right)}\, dx
Integral(tan(x)^2, (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

    tan2(x)=sec2(x)1\tan^{2}{\left(x \right)} = \sec^{2}{\left(x \right)} - 1

  2. Integrate term-by-term:

    1. sec2(x)dx=tan(x)\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}

    1. The integral of a constant is the constant times the variable of integration:

      (1)dx=x\int \left(-1\right)\, dx = - x

    The result is: x+tan(x)- x + \tan{\left(x \right)}

  3. Add the constant of integration:

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


The answer is:

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

The answer (Indefinite) [src]
  /                           
 |                            
 |    2                       
 | tan (x) dx = C - x + tan(x)
 |                            
/                             
tan2(x)dx=Cx+tan(x)\int \tan^{2}{\left(x \right)}\, dx = C - x + \tan{\left(x \right)}
The graph
0.001.000.100.200.300.400.500.600.700.800.900.02.5
The answer [src]
     sin(1)
-1 + ------
     cos(1)
1+sin(1)cos(1)-1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}
=
=
     sin(1)
-1 + ------
     cos(1)
1+sin(1)cos(1)-1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}
-1 + sin(1)/cos(1)
Numerical answer [src]
0.557407724654902
0.557407724654902
The graph
Integral of tg²xdx dx

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