If int((sin^((3)/(2))x+cos^((3)/(2))x)dx...

If `int((sin^((3)/(2))x+cos^((3)/(2))x)dx)/(sqrt(sin^(3)x cos^(3)x sin(x-alpha)))=a sqrt(cos alpha tan x-sin alpha)+b sqrt(cos alpha-sin alpha cot x)+c` then

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Evaluate: int((sin^((3)/(2))x+cos^((3)/(2))x)dx)/(sqrt(sin^(3)x cos^(3)x sin(x-alpha)))=

(1)/(sqrt(sin^(3)x sin(x+alpha)))

(1)/(sqrt(sin^(3)x.sin(x+alpha)))

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

int sqrt((sin(x-alpha))/(sin(x+alpha)))

If x=a sin alpha+b cos alpha and y=a cos alpha-b sin alpha then remove alpha

lim_(x rarr oo)sqrt((x+cos alpha)/(x+sin alpha))=

int(cos2x-cos2 alpha)/(sin x-sin alpha)dx=