Evaluate : ∫ ( x 2 + 1 ) ( x 2 + 3 ) x 3 + 3 x 2 + x + 9 d x

∫ ( x 2 + 1 ) ( x 2 + 3 ) x 3 + 3 x 2 + x + 9 d x = ∫ x 2 + 3 x d x + 3 ∫ x 2 + 1 d x = 2 1 ℓ n x 2 + 3 + 3 tan − 1 x + c

Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationMiscellaneous formMedium2 minQB

MathematicsMediumsingle choice

Evaluate : $\int \frac{x ^{3} + 3 x ^{2} + x + 9}{( x ^{2} + 1 ) ( x ^{2} + 3 )} d x$

Answer:

Solution:

$\int \frac{x ^{3} + 3 x ^{2} + x + 9}{( x ^{2} + 1 ) ( x ^{2} + 3 )} d x = \int \frac{x}{x ^{2} + 3} d x + 3 \int \frac{d x}{x ^{2} + 1}$

$= \frac{1}{2} ℓ n x^{2} + 3 + 3 tan^{- 1} x + c$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Miscellaneous form

⏱ 2mℹ️ Source: QB

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