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```         integrel of(1-cot^(n-2)x)dx
--------------------
tanx+cotx.cot^(n-2)x
integral of 3+2cosx dx
-----------
(2+3cosx)^2
integral of       dx
------------------
(1+x^0.5)(x-x^2)^0.5```
7 years ago

Chetan Mandayam Nayakar
312 Points
```										(1+x^0.5)(x-x^2)^0.5 dx = I
let x = sin2(q)
I = 2sin2(q)cos2(q)(1+sin(q)) dq
= ((sin2(2q)/2)dq+ 2 cos2(q)(1-cos2(q))dq
= (1-cos(4(theta))) d(theta) + 2cos2(q)sin(theta) d(theta) -  2cos4(q)sin(theta) d(theta)
I= (theta/4) –(sin(4(theta))/16) +((2/5)cos5(q)) - ((2/3)cos3(q))
q = arcsin(sqrt(x))
```
7 years ago
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