Integral of -tan(x) dx

You have entered [src]

  1           
  /           
 |            
 |  -tan(x) dx
 |            
/             
0

$$\int\limits_{0}^{1} \left(- \tan{\left(x \right)}\right)\, dx$$

Integral(-tan(x), (x, 0, 1))

Detail solution

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

$\int \left(- \tan{\left(x \right)}\right)\, dx = - \int \tan{\left(x \right)}\, dx$
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 $- du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{u}\right)\, du = - \int \frac{1}{u}\, du$
    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: $\log{\left(\cos{\left(x \right)} \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                            
 |                             
 | -tan(x) dx = C + log(cos(x))
 |                             
/

$$-\log \sec x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

log(cos(1))

$$\log \cos 1$$

log(cos(1))

$$\log{\left(\cos{\left(1 \right)} \right)}$$

Упростить

Numerical answer [src]

-0.615626470386014

-0.615626470386014

The graph

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