Mathematics

# $\int (1 + 2x + 3x^2 + 4x^3 + ...)dx =$

##### ANSWER

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

##### SOLUTION
$\displaystyle \int(1+2x+3x^2+4x^3+..)dx$
$=\displaystyle \int (1-x)^2dx\quad [(1-x)^2=1+2x+3x^2]$
$=\int \dfrac{dx}{\left(1-x\right)^2}$
$=(1-x)^{-1}+c$
$\therefore \boxed\int(1+2x+3x^2+.....)dx}=(1-x)^{-1}+$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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