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![For real numbers &, p, Yand &, if 2ex +3e X Moge(4ex 7e^)) dx = (ux 81. |f (x2 _ 1) + tan-1 x2+1 14 4ex +7e-x a constant of integration, then C where Cis dx (Main) 2021] [JEE U+ vis equal to ( x4 +3x2 + 1)tan' 1 2x+1 2x+1 dx atan +b J +C 17(2_1) ) 82. If x2 +1 (x2 +x+1)2 X2+ X+1 3 aloge ptan' tan + X > 0 where Cis the constant of integration then 2+1 +C Stan the value of 9 V3a+ b is equal to Where Cis an arbitrary constant then the value of [JEE (Main)-2021] BY + S) is equal to 10(0 [JEE (Main) 2021] sin X +Bloge dloge I1+tanx| dx = 83. Ifl sin? X+ cos3 x 5x8 +7x6 f(x) = J dx, (X >0), f(0) = 0 and f 0 (x2+1+2x7)2 2tanx-1 |1- tan x + tanfx | +ytan -1 +C when V3 f(1) = then the value of Kis K C is constant of integration, then the value of 18(0 + p + 12) is [JEE (Main) 2021] [JEE (Main)-2021] For real numbers &, p, Yand &, if 2ex +3e X Moge(4ex 7e^)) dx = (ux 81. |f (x2 _ 1) + tan-1 x2+1 14 4ex +7e-x a constant of integration, then C where Cis dx (Main) 2021] [JEE U+ vis equal to ( x4 +3x2 + 1)tan' 1 2x+1 2x+1 dx atan +b J +C 17(2_1) ) 82. If x2 +1 (x2 +x+1)2 X2+ X+1 3 aloge ptan' tan + X > 0 where Cis the constant of integration then 2+1 +C Stan the value of 9 V3a+ b is equal to Where Cis an arbitrary constant then the value of [JEE (Main)-2021] BY + S) is equal to 10(0 [JEE (Main) 2021] sin X +Bloge dloge I1+tanx| dx = 83. Ifl sin? X+ cos3 x 5x8 +7x6 f(x) = J dx, (X >0), f(0) = 0 and f 0 (x2+1+2x7)2 2tanx-1 |1- tan x + tanfx | +ytan -1 +C when V3 f(1) = then the value of Kis K C is constant of integration, then the value of 18(0 + p + 12) is [JEE (Main) 2021] [JEE (Main)-2021]](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_568055_1fef7fb3_1776938529774_sc.jpg?tenant=sc&referrer=feed-service&f=774_sc.jpg)
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