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Identical expressions
five /sin^2x- seven
5 divide by sinus of squared x minus 7
five divide by sinus of squared x minus seven
5/sin2x-7
5/sin²x-7
5/sin to the power of 2x-7
5 divide by sin^2x-7
5/sin^2x-7dx
Similar expressions
5/sin^2x+7

Solving integrals/ 5/sin^2x-7

Integral of 5/sin^2x-7 dx

The solution

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  1                 
  /                 
 |                  
 |  /   5       \   
 |  |------- - 7| dx
 |  |   2       |   
 |  \sin (x)    /   
 |                  
/                   
0

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

Integral(5/sin(x)^2 - 7, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-7\right)\, dx = - 7 x$
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: $- 7 x - \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

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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]

6.89661838974298e+19

6.89661838974298e+19

The graph

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

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Integral of 5/sin^2x-7 dx

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Piecewise:

The solution