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Integral of d{x}:
Integral of e^(x^4)*x^3
Integral of sinxcos2x
Integral of cos4x/sin^34x
Integral of 9/(x^2+9)
Identical expressions
cos4x/sin^34x
co sinus of e of 4x divide by sinus of cubed 4x
cos4x/sin34x
cos4x/sin³4x
cos4x/sin to the power of 34x
cos4x divide by sin^34x
cos4x/sin^34xdx

Solving integrals/ cos4x/sin^34x

Integral of cos4x/sin^34x dx

The solution

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  1             
  /             
 |              
 |   cos(4*x)   
 |  --------- dx
 |     3        
 |  sin (4*x)   
 |              
/               
0

$$\int\limits_{0}^{1} \frac{\cos{\left(4 x \right)}}{\sin^{3}{\left(4 x \right)}}\, dx$$

Integral(cos(4*x)/(sin(4*x)^3), (x, 0, 1))

Detail solution

Let $u = 4 x$ .

Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :

$\int \frac{\cos{\left(u \right)}}{16 \sin^{3}{\left(u \right)}}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(u \right)}}{4 \sin^{3}{\left(u \right)}}\, du = \frac{\int \frac{\cos{\left(u \right)}}{\sin^{3}{\left(u \right)}}\, du}{4}$
  1. Let $u = \sin{\left(u \right)}$ .
    
    Then let $du = \cos{\left(u \right)} du$ and substitute $du$ :
    
    $\int \frac{1}{u^{3}}\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{u^{3}}\, du = - \frac{1}{2 u^{2}}$
    Now substitute $u$ back in:
    
    $- \frac{1}{2 \sin^{2}{\left(u \right)}}$
  So, the result is: $- \frac{1}{8 \sin^{2}{\left(u \right)}}$
Now substitute $u$ back in:

$- \frac{1}{8 \sin^{2}{\left(4 x \right)}}$
Add the constant of integration:

$- \frac{1}{8 \sin^{2}{\left(4 x \right)}}+ \mathrm{constant}$

The answer is:

$- \frac{1}{8 \sin^{2}{\left(4 x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 |  cos(4*x)               1     
 | --------- dx = C - -----------
 |    3                    2     
 | sin (4*x)          8*sin (4*x)
 |                               
/

$$-{{1}\over{8\,\sin ^2\left(4\,x\right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$${\it \%a}$$

nan

$$\text{NaN}$$

Simplify

Numerical answer [src]

1.43025787172421e+36

1.43025787172421e+36

The graph

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

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Identical expressions

Integral of cos4x/sin^34x dx

Limits of integration:

The graph:

Piecewise:

The solution