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Identical expressions
(seven *sin^3x+ five)/sin^2x
(7 multiply by sinus of cubed x plus 5) divide by sinus of squared x
(seven multiply by sinus of cubed x plus five) divide by sinus of squared x
(7*sin3x+5)/sin2x
7*sin3x+5/sin2x
(7*sin³x+5)/sin²x
(7*sin to the power of 3x+5)/sin to the power of 2x
(7sin^3x+5)/sin^2x
(7sin3x+5)/sin2x
7sin3x+5/sin2x
7sin^3x+5/sin^2x
(7*sin^3x+5) divide by sin^2x
(7*sin^3x+5)/sin^2xdx
Similar expressions
(7*sin^3x-5)/sin^2x

Integral of (7*sin^3x+5)/sin^2x dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |       3          
 |  7*sin (x) + 5   
 |  ------------- dx
 |        2         
 |     sin (x)      
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{7 \sin^{3}{\left(x \right)} + 5}{\sin^{2}{\left(x \right)}}\, dx$$

Integral((7*sin(x)^3 + 5)/sin(x)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{7 \sin^{3}{\left(x \right)} + 5}{\sin^{2}{\left(x \right)}} = \frac{7 \sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{5}{\sin^{2}{\left(x \right)}}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{7 \sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx = 7 \int \frac{\sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \cos{\left(x \right)}$
  So, the result is: $- 7 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{5}{\sin^{2}{\left(x \right)}}\, dx = 5 \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  So, the result is: $- \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $- 7 \cos{\left(x \right)} - \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$- \frac{7 \sin{\left(x \right)} + 5}{\tan{\left(x \right)}}$
Add the constant of integration:

$- \frac{7 \sin{\left(x \right)} + 5}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- \frac{7 \sin{\left(x \right)} + 5}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                          
 |                                           
 |      3                                    
 | 7*sin (x) + 5                     5*cos(x)
 | ------------- dx = C - 7*cos(x) - --------
 |       2                            sin(x) 
 |    sin (x)                                
 |                                           
/

$$\int \frac{7 \sin^{3}{\left(x \right)} + 5}{\sin^{2}{\left(x \right)}}\, dx = C - 7 \cos{\left(x \right)} - \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

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Numerical answer [src]

6.89661838974298e+19

6.89661838974298e+19

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

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Identical expressions

Similar expressions

Integral of (7*sin^3x+5)/sin^2x dx

Limits of integration:

The graph:

Piecewise:

The solution