Indefinite Integration

Ques1) If f (3x-4 / 3x+4 ) = x+2 then show that ∫ f(x) dx is -8/3 log 3 |1-x| + 2/3 x +c

Ques2) If ∫ x log (1 +1/x) dx = f(x) ln (x+1) + g(x) ln x^2 +Lx +c, then choose the correct alternative/s
(a)f(x) = x^2 /2 (b)g(x) = ln x
(c)L=1 (d)L=1/2

3 Answers

62
Lokesh Verma ·

3x-4/3x+4 = t

then find x =4/3 (t+1)/(t-1)

Now question 1 is done :)

62
Lokesh Verma ·

x log (x+1) - x log x

then use by parts :)

11
Tush Watts ·

Thanx a lot Nishant sir for your hint.
Let me try

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