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Q.

If f3x−43x+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

answer is B.

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Detailed Solution

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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