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If 5 x dx = x cosec x (cosec2 x + 32 ) + e | x2 | + C where , R and C is the constant of integration, then the value of 8( + ) equals .
1
In = n-2x cosec2 x dx; by parts, then 2 x = cosec2 x - 1:
In = - cosecn-2x xn - 1 + n - 2n - 1In-2
n = 5: I5 = - 14 x cosec3 x + 34I3
n = 3: I3 = - 12 x cosec x + 12 e | x2 |
I5 = - 14 x cosec x (cosec2 x + 32 ) + 38 e | x2 | + C
= - 14, = 38 8( + ) = -2 + 3 = 1
Answer: 1
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