_ ^ (1 + 2x + 3 x^2 + 4 x^3 + ......) ;dx = - Vidyadip

MCQ

$\int_{}^{} {(1 + 2x + 3{x^2} + 4{x^3} + ......)\;dx = } $

A
${(1 + x)^{ - 1}} + c$
✓
${(1 - x)^{ - 1}} + c$
C
${(1 - x)^{ - 1}} - 1 + c$
D
None of these

✓

Answer

Correct option: B.

${(1 - x)^{ - 1}} + c$

b
(b)$\int_{}^{} {(1 + 2x + 3{x^2} + 4{x^3} + ......)\,dx} $
$ = \int_{}^{} {{{(1 - x)}^{ - 2}}dx = {{(1 - x)}^{ - 1}} + c.} $

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