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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

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

Grade:

1 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

(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))

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