If ∫ x + x 7 d x = p ( x ) then, ∫ x + x 7 x 6 d x is equal to:

∫ x + x 7 x 6 d x = ∫ x ( 1 + x 6 ) x 6 d x = ∫ x ( 1 + x 6 ) ( 1 + x 6 ) − 1 d x = ∫ x 1 d x − ∫ x + x 7 1 d x = ln ∣ x ∣ − p ( x ) + c

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 minPYQ_2013

MathematicsMediumsingle choice

If $\int \frac{d x}{x + x ^{7}} = p (x)$ then, $\int \frac{x ^{6}}{x + x ^{7}} d x$ is equal to:

Options:

Answer:

Solution:

$\int \frac{x ^{6}}{x + x ^{7}} d x = \int \frac{x ^{6}}{x ( 1 + x ^{6} )} d x$ $= \int \frac{( 1 + x ^{6} ) - 1}{x ( 1 + x ^{6} )} d x$ $= \int \frac{1}{x} d x - \int \frac{1}{x + x ^{7}} d x$ $= ln ∣ x ∣ - p (x) + c$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2013

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