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((1+tgx)/(1-tgx))*dx

Integral of ((1+tgx)/(1-tgx))*dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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  1                             
  /                             
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 |                   1          
 |  (1 + tan(x))*----------*1 dx
 |               1 - tan(x)     
 |                              
/                               
0                               
$$\int\limits_{0}^{1} \left(\tan{\left(x \right)} + 1\right) \frac{1}{1 - \tan{\left(x \right)}} 1\, dx$$
Integral((1 + tan(x))*1/(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                 log\1 + tan (x)/                   
 | (1 + tan(x))*----------*1 dx = C + ---------------- - log(-1 + tan(x))
 |              1 - tan(x)                   2                           
 |                                                                       
/                                                                        
$$\int \left(\tan{\left(x \right)} + 1\right) \frac{1}{1 - \tan{\left(x \right)}} 1\, dx = C - \log{\left(\tan{\left(x \right)} - 1 \right)} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2}$$
The graph
The answer [src]
nan
$$\text{NaN}$$
=
=
nan
$$\text{NaN}$$
Numerical answer [src]
-1.5989832649916
-1.5989832649916
The graph
Integral of ((1+tgx)/(1-tgx))*dx dx

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