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If int(sinx)^(- 3/4)(cosx)^(-21/4)dx=(ta...

If `int(sinx)^(- 3/4)(cosx)^(-21/4)dx=(tanx)^(a_(1))/b_1+((tanx)^(a_(2)))/b_2+((tanx)^(a_(3)))/b_3+C.` where C is integration constant , then `[(a_1+a_2+a_3+b_1+b_2+b_3)/2]` (where [*]denotes greatest integer function) equals to : (A)3 (B) 4 (C) 5 (D) 7

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If int(sin x)^((-3)/(4))(cos x)^((-21)/(4))dx=((tan x)^(a_(1)))/(b_(1))+((tan x)^(a_(2)))/(b_(2))+((tan x)^(a_(3)))/(b_(3)) where C is integration constant then [(a_(1)+a_(2)+a_(3)+b_(1)+b_(2)+b_(3))/(2)] equals.( [.] denotes greatest integer function).

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Let log_2N=a_1+b_1,log_3N=a_2+b_2 and log_5N=a_3+b_3 , where a_1,a_2,a_3notin1 and b_1,b_2 b_3 in [0,1) . If a_1=6,a_2=4 and a_3=3 ,the difference of largest and smallest integral values of N, is