Mister Exam

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Integral of cosx/(3√sin^2x)
Identical expressions
cosx/(three √sin^2x)
co sinus of e of x divide by (3√ sinus of squared x)
co sinus of e of x divide by (three √ sinus of squared x)
cosx/(3√sin2x)
cosx/3√sin2x
cosx/(3√sin²x)
cosx/(3√sin to the power of 2x)
cosx/3√sin^2x
cosx divide by (3√sin^2x)
cosx/(3√sin^2x)dx

Integral of cosx/(3√sin^2x) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |      cos(x)      
 |  ------------- dx
 |              2   
 |      ________    
 |  3*\/ sin(x)     
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{3 \left(\sqrt{\sin{\left(x \right)}}\right)^{2}}\, dx$$

Integral(cos(x)/((3*(sqrt(sin(x)))^2)), (x, 0, 1))

Detail solution

Let $u = 3 \left(\sqrt{\sin{\left(x \right)}}\right)^{2}$ .

Then let $du = 3 \cos{\left(x \right)} dx$ and substitute $\frac{du}{3}$ :

$\int \frac{1}{3 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{3}$
Now substitute $u$ back in:

$\frac{\log{\left(3 \left(\sqrt{\sin{\left(x \right)}}\right)^{2} \right)}}{3}$
Now simplify:

$\frac{\log{\left(3 \sin{\left(x \right)} \right)}}{3}$
Add the constant of integration:

$\frac{\log{\left(3 \sin{\left(x \right)} \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(3 \sin{\left(x \right)} \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          /            2\
 |                           |    ________ |
 |     cos(x)             log\3*\/ sin(x)  /
 | ------------- dx = C + ------------------
 |             2                  3         
 |     ________                             
 | 3*\/ sin(x)                              
 |                                          
/

$$\int \frac{\cos{\left(x \right)}}{3 \left(\sqrt{\sin{\left(x \right)}}\right)^{2}}\, dx = C + \frac{\log{\left(3 \left(\sqrt{\sin{\left(x \right)}}\right)^{2} \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

14.6392807959079

14.6392807959079

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

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Identical expressions

Integral of cosx/(3√sin^2x) dx

Limits of integration:

The graph:

Piecewise:

The solution