Mister Exam

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Solving integrals/ dx/sinxcosx

Integral of dx/sinxcosx dx

The solution

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  1          
  /          
 |           
 |  cos(x)   
 |  ------ dx
 |  sin(x)   
 |           
/            
0

$$\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\, dx$$

Integral(cos(x)/sin(x), (x, 0, 1))

Detail solution

Let $u = \sin{\left(x \right)}$ .

Then let $du = \cos{\left(x \right)} dx$ and substitute $du$ :

$\int \frac{1}{u}\, du$
1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
Now substitute $u$ back in:

$\log{\left(\sin{\left(x \right)} \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\, dx = C + \log{\left(\sin{\left(x \right)} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

43.9178423877238

43.9178423877238

The graph

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

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Identical expressions

Similar expressions

Integral of dx/sinxcosx dx

Limits of integration:

The graph:

Piecewise:

The solution