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Similar expressions
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Solving integrals/ (1+ctgx)/sin^2x

Integral of (1+ctgx)/sin^2x dx

The solution

You have entered [src]

 pi              
 --              
 2               
  /              
 |               
 |  1 + cot(x)   
 |  ---------- dx
 |      2        
 |   sin (x)     
 |               
/                
0

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

Integral((1 + cot(x))/(sin(x)^2), (x, 0, pi/2))

Detail solution

Rewrite the integrand:

$\frac{\cot{\left(x \right)} + 1}{\sin^{2}{\left(x \right)}} = \frac{\cot{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{\sin^{2}{\left(x \right)}}$
Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \frac{1}{2 \sin^{2}{\left(x \right)}}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{1}{2 \sin^{2}{\left(x \right)}}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$-{{\left({{1}\over{\tan x}}+1\right)^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

Simplify

Numerical answer [src]

3.70857358997728e+37

3.70857358997728e+37

The graph

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

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Identical expressions

Similar expressions

Integral of (1+ctgx)/sin^2x dx

Limits of integration:

The graph:

Piecewise:

The solution