Mister Exam

Other calculators

Solving integrals/ 1/(sin^2x-sin^4x)

Integral of 1/(sin^2x-sin^4x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  p                     
  -                     
  3                     
  /                     
 |                      
 |          1           
 |  ----------------- dx
 |     2         4      
 |  sin (x) - sin (x)   
 |                      
/                       
p                       
-                       
6
∫p6p31−sin⁡4(x)+sin⁡2(x) dx\int\limits_{\frac{p}{6}}^{\frac{p}{3}} \frac{1}{- \sin^{4}{\left(x \right)} + \sin^{2}{\left(x \right)}}\, dx 
Integral(1/(sin(x)^2 - sin(x)^4), (x, p/6, p/3))
The answer (Indefinite) [src] 
  /                                                              4/x\                      2/x\       
 |                                                            tan |-|                 6*tan |-|       
 |         1                            1                         \2/                       \2/       
 | ----------------- dx = C + ---------------------- + ---------------------- - ----------------------
 |    2         4                    /x\        3/x\          /x\        3/x\          /x\        3/x\
 | sin (x) - sin (x)          - 2*tan|-| + 2*tan |-|   - 2*tan|-| + 2*tan |-|   - 2*tan|-| + 2*tan |-|
 |                                   \2/         \2/          \2/         \2/          \2/         \2/
/
∫1−sin⁡4(x)+sin⁡2(x) dx=C+tan⁡4(x2)2tan⁡3(x2)−2tan⁡(x2)−6tan⁡2(x2)2tan⁡3(x2)−2tan⁡(x2)+12tan⁡3(x2)−2tan⁡(x2)\int \frac{1}{- \sin^{4}{\left(x \right)} + \sin^{2}{\left(x \right)}}\, dx = C + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} - \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} + \frac{1}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}}
Simplify

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

    © Mister Exam – Calculator