Mathematics

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


ANSWER

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


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

















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Single Correct Medium Published on 17th 09, 2020
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