Integral of 3tg(x) dx

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 |  3*tan(x) dx
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$$\int\limits_{0}^{20} 3 \tan{\left(x \right)}\, dx$$

Integral(3*tan(x), (x, 0, 20))

Detail solution

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

$\int 3 \tan{\left(x \right)}\, dx = 3 \int \tan{\left(x \right)}\, dx$
1. Rewrite the integrand:
  
  $\tan{\left(x \right)} = \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
2. Let $u = \cos{\left(x \right)}$ .
  
  Then let $du = - \sin{\left(x \right)} dx$ and substitute $- du$ :
  
  $\int \left(- \frac{1}{u}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{u}\, du = - \int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $- \log{\left(u \right)}$
  Now substitute $u$ back in:
  
  $- \log{\left(\cos{\left(x \right)} \right)}$
So, the result is: $- 3 \log{\left(\cos{\left(x \right)} \right)}$
Add the constant of integration:

$- 3 \log{\left(\cos{\left(x \right)} \right)}+ \mathrm{constant}$

The answer is:

$- 3 \log{\left(\cos{\left(x \right)} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | 3*tan(x) dx = C - 3*log(cos(x))
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$$\int 3 \tan{\left(x \right)}\, dx = C - 3 \log{\left(\cos{\left(x \right)} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

Numerical answer [src]

8.87919148092043

8.87919148092043

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