Indefinite IntegrationHard
Question
The value of ∫etan-1 x 
dx is equal to
dx is equal toOptions
A.x etan-1x + C
B.x2 etan-1 x + C
C.1/x etan-1 x + C
D.none of these
Solution
Let tan-1x = t ⇒ 
dx = dt
I = ∫et(sec2t + tan t)dt = et tan t + C
= x etan-1 + C
dx = dtI = ∫et(sec2t + tan t)dt = et tan t + C
= x etan-1 + C
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