Integration.(JEE)

Question

( \int e^{2 x}\left(x^{3}+x^{2}-x+1\right) d x=\frac{e^{2 x}}{8} p(x)+C \), where \( p(x) \) is a cubic polynomial and \( C \) is arbitrary constant of integration. Then \( p(x)= \) 1) \( 4 x^{3}-2 x^{2}-2 x+5 \) 2) \( 4 x^{3}+2 x^{2}-2 x+5 \) 3) \( 4 x^{3}-2 x^{2}+2 x+5 \) 4) \( 4 x^{3}+2 x^{2}+2 x+5 \)

Answer 1

p(x) = 1) 4x³ − 2x² − 2x + 5

Comments

How ?

Answer 2

The correct answer is (1)

Comments

Can u please tell me when this trick is applicable. I didnt get in which type of question i can use this .

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Basically you can use this trick in
Exponential×polynomial or trigonometry×polynomial functions only