Mister Exam

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2/(sinxcosx)dx

Integral of 2/(sinxcosx) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |        2         
 |  ------------- dx
 |  sin(x)*cos(x)   
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{2}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx$$

Integral(2/((sin(x)*cos(x))), (x, 0, 1))

Detail solution

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

$\int \frac{2}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx = 2 \int \frac{1}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \frac{\log{\left(\sin^{2}{\left(x \right)} - 1 \right)}}{2} + \log{\left(\sin{\left(x \right)} \right)}$
So, the result is: $- \log{\left(\sin^{2}{\left(x \right)} - 1 \right)} + 2 \log{\left(\sin{\left(x \right)} \right)}$
Now simplify:

$2 \log{\left(\sin{\left(x \right)} \right)} - \log{\left(- \cos^{2}{\left(x \right)} \right)}$
Add the constant of integration:

$2 \log{\left(\sin{\left(x \right)} \right)} - \log{\left(- \cos^{2}{\left(x \right)} \right)}+ \mathrm{constant}$

The answer is:

$2 \log{\left(\sin{\left(x \right)} \right)} - \log{\left(- \cos^{2}{\left(x \right)} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                        
 |                                                         
 |       2                   /        2   \                
 | ------------- dx = C - log\-1 + sin (x)/ + 2*log(sin(x))
 | sin(x)*cos(x)                                           
 |                                                         
/

$$\int \frac{2}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx = C - \log{\left(\sin^{2}{\left(x \right)} - 1 \right)} + 2 \log{\left(\sin{\left(x \right)} \right)}$$

Simplify

The answer [src]

oo - pi*I

$$\infty - i \pi$$

oo - pi*I

$$\infty - i \pi$$

Упростить

Numerical answer [src]

89.0669377162196

89.0669377162196

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

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Identical expressions

Integral of 2/(sinxcosx) dx

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The solution