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Integral of 12*tg(x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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  5             
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 |  12*tan(x) dx
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$$\int\limits_{3}^{5} 12 \tan{\left(x \right)}\, dx$$
Integral(12*tan(x), (x, 3, 5))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Rewrite the integrand:

    2. Let .

      Then let and substitute :

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

        1. The integral of is .

        So, the result is:

      Now substitute back in:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
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 | 12*tan(x) dx = C - 12*log(cos(x))
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$$\int 12 \tan{\left(x \right)}\, dx = C - 12 \log{\left(\cos{\left(x \right)} \right)}$$
The graph
The answer [src]
nan
$$\text{NaN}$$
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nan
$$\text{NaN}$$
nan
Numerical answer [src]
-1.23245692718491
-1.23245692718491

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