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Solving integrals/ dx/(sin(x)+cos(x))^2

Integral of dx/(sin(x)+cos(x))^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                      
 --                      
 3                       
  /                      
 |                       
 |          1            
 |  ------------------ dx
 |                   2   
 |  (sin(x) + cos(x))    
 |                       
/                        
0
∫0π31(sin⁡(x)+cos⁡(x))2 dx\int\limits_{0}^{\frac{\pi}{3}} \frac{1}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}\, dx 
Integral(1/((sin(x) + cos(x))^2), (x, 0, pi/3))
The answer (Indefinite) [src] 
  /                                         /x\       
 |                                     2*tan|-|       
 |         1                                \2/       
 | ------------------ dx = C - -----------------------
 |                  2                  2/x\        /x\
 | (sin(x) + cos(x))           -1 + tan |-| - 2*tan|-|
 |                                      \2/        \2/
/
∫1(sin⁡(x)+cos⁡(x))2 dx=C−2tan⁡(x2)tan⁡2(x2)−2tan⁡(x2)−1\int \frac{1}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}\, dx = C - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1}
Simplify
The graph
0.000.100.200.300.400.500.600.700.800.901.0002
Plot the graph f(x)
The answer [src] 
          ___    
     -2*\/ 3     
-----------------
  /          ___\
  |  2   2*\/ 3 |
3*|- - - -------|
  \  3      3   /
−233(−233−23)- \frac{2 \sqrt{3}}{3 \left(- \frac{2 \sqrt{3}}{3} - \frac{2}{3}\right)} 
=
= 
          ___    
     -2*\/ 3     
-----------------
  /          ___\
  |  2   2*\/ 3 |
3*|- - - -------|
  \  3      3   /
−233(−233−23)- \frac{2 \sqrt{3}}{3 \left(- \frac{2 \sqrt{3}}{3} - \frac{2}{3}\right)} 
-2*sqrt(3)/(3*(-2/3 - 2*sqrt(3)/3))
Numerical answer [src] 
0.633974596215561
0.633974596215561

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

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