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Q.

∫03dxx+1+5x+1=

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a

12ln(95)

b

1+ln(95)

c

1+12ln(95)

d

1+14ln(95)

answer is D.

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Detailed Solution

∫03dxx+1+5x+1=∫035x+1−x+14xdx =14∫035x+1xdx−14∫03x+1xdxSetting 5x+1=t2 in the first integral and x+1=t2 in the second integral,12∫14t2t2−1dt−12∫12t2t2−1dt=12∫24t2t2−1dt =12∫24(1+1t2−1)dt =1+14lnt−1t+1|24=1+14log(95)

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