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Let 2 - x3 + x dx = 12 ( x + e| x + x| ) + C, where C is the constant of integration. Then + is equal to :
(4) 4
I = 2 x - x3 x + x dx
Write numerator = A(denominator) + B(derivative of denominator):
2 x - x = A(3 x + x) + B( x - 3 x)
3A + B = 2, A - 3B = -1 A = B = 12
I = 12x + 12 e|3 x + x| + C = 12 (x + e| x + 3 x| ) + C
Comparing: = 1 and : = 3 : 1, so + = 1 + 3 = 4
Answer: (4)
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