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(1+tg(x))/(1-tg(x))

Integral of (1+tg(x))/(1-tg(x)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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  1              
  /              
 |               
 |  1 + tan(x)   
 |  ---------- dx
 |  1 - tan(x)   
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{\tan{\left(x \right)} + 1}{- \tan{\left(x \right)} + 1}\, dx$$
Integral((1 + tan(x))/(1 - tan(x)), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. Rewrite the integrand:

    3. Integrate term-by-term:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. Don't know the steps in finding this integral.

          But the integral is

        So, the result is:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. Don't know the steps in finding this integral.

          But the integral is

        So, the result is:

      The result is:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Rewrite the integrand:

      2. The integral of a constant times a function is the constant times the integral of the function:

        1. Don't know the steps in finding this integral.

          But the integral is

        So, the result is:

      1. Rewrite the integrand:

      2. The integral of a constant times a function is the constant times the integral of the function:

        1. Don't know the steps in finding this integral.

          But the integral is

        So, the result is:

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                       
 |                        /       2   \                   
 | 1 + tan(x)          log\1 + tan (x)/                   
 | ---------- dx = C + ---------------- - log(-1 + tan(x))
 | 1 - tan(x)                 2                           
 |                                                        
/                                                         
$${{\log \left(\tan ^2x+1\right)}\over{2}}-\log \left(\tan x-1\right)$$
The graph
The answer [src]
nan
$${{\log \left(\tan ^21+1\right)}\over{2}}-\log \left(\tan 1-1\right)$$
=
=
nan
$$\text{NaN}$$
Numerical answer [src]
-1.5989832649916
-1.5989832649916
The graph
Integral of (1+tg(x))/(1-tg(x)) dx

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