Indefinite Integration 1 Question 89

90. If α=01(e9x+3tan1x)12+9x21+x2dx,

where tan1x takes only principal values, then the value of loge|1+α|3π4 is

(2015 Adv.)

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Answer:

Correct Answer: 90. (9)

Solution:

  1. Here, α=01e(9x+3tan1x)12+9x21+x2dx

Put 9x+3tan1x=t

9+31+x2dx=dt

α=09+3π/4etdt=[et]09+3π/4=e9+3π/41

loge|1+α|=9+3π4

loge|α+1|3π4=9



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