By the inspection method, evaluate: ( a u 2 + b u + c ) d u

Question

By the inspection method, evaluate:

$\int (a u^{2} + b u + c) d u$

Smart Achievers · Accepted Answer

(1)

Ans. $a (\frac{u^{3}}{3}) + b (\frac{u^{2}}{2}) + c u + C$

Explanation:

The given integral is $\int (a u^{2} + b u + c) d u$

$\int (a u^{2} + b u + c) d u = \int a u^{2} d u + \int b u d u + \int c d u$

$= a \int u^{2} d u + b \int u d u + c \int d u$

$= a (\frac{u^{3}}{3}) + b (\frac{u^{2}}{2}) + c u + C$

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