First slide

Introduction to integration

Question

$\int (1 + 2 x + 3 x^{2} + 4 x^{3} + \dots) d x =$

Easy

A

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

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

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

$None of these$

Solution

$\begin{aligned} \int (1 + 2 x + 3 x^{2} + 4 x^{3} + \dots) d x = \int (1 - x)^{- 2} d x \\ = (1 - x)^{- 1} + c \end{aligned}$

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