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If f3x43x+4=x+2, then f(x)dx is 

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a
ex+2log⁡3x−43x+4+c
b
−83log⁡|1−x|+23x+c
c
83log⁡|1−x|+x3+c
d
e[(3x−4)(3x+4)]−x22−2x+c

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detailed solution

Correct option is B

Put x=3t−43t+4=1−83t+4,dx=24(3t+4)2dtNow ∫f(x)dx=∫f3t−43t+424(3t+4)2dt=∫t+2(3t+4)2(24)dt=8∫3t+4+2(3t+4)2dt=8∫13t+4+2(3t+4)2dt=83log⁡|3t+4|−2383t+4+C1=83log⁡81−x−23(1−x)+C1=−83log⁡|1−x|+23x+C


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