Integral Calculus Question 274

Question: $ \int_{{}}^{{}}{(1+2x+3x^{2}+4x^{3}+……)\ dx=} $

Options:

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

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

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

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

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