If y = x²/1+x², ∫ y dx = C + f, f = ______?
- x - 1 + 1/(x+1)
- x + 1 + 1/(x+1)
- x - 1 + 1/(x-1)
- None of these
Explanation
Given y = x²/(1 + x²),
∫y dx = ∫[x²/(1 + x²)] dx = ∫[1 - 1/(1 + x²)] dx = x - arctan(x) + C.
Given ∫y dx = C + f, f = x - arctan(x).
x - 1 + 1/(x + 1)
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