Indefinite IntegrationHard

Question

The value of ∫x. dx equals:

Options

A. - x + C
B.
C.
D. + x + C

Solution


I =
= ln(x + ) -      (using integration by parts)
= ln(x + ) - x + C
Alternate:
Let x + = et then - x = e- t
 = dt = dt
I = ∫x t dt =
= t(et + e- t) - (et - e- t) + C
= ln (x + ) - x + C.

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