The integral ∫ 2 − x 2 + 2 − x 2 x d x equals :

I = ∫ 2 − x 2 + 2 − x 2 x d x Put t = 2 − x 2 , d x d t = 2 2 − x 2 1 ⋅ ( − 2 x ) ⇒ − t d t = x d x ∴ I = ∫ t 2 + t ( − t ) d t = − ∫ t + 1 1 d t = − lo g ∣ t + 1∣ = − lo g 2 − x 2 + 1 + c

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 minPYQ_2013

MathematicsMediumsingle choice

The integral $\int \frac{x d x}{2 - x ^{2} + 2 - x ^{2}}$ equals :

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Solution:

$I = \int \frac{x d x}{2 - x ^{2} + 2 - x ^{2}}$ $Put t = 2 - x^{2}, \frac{d t}{d x} = \frac{1}{2 2 - x ^{2}} \cdot (- 2 x) \Rightarrow - t d t = x d x ∴ I = \int \frac{( - t ) d t}{t ^{2} + t} = - \int \frac{1}{t + 1} d t = - lo g ∣ t + 1∣ = - lo g 2 - x^{2} + 1 + c$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2013

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