∫ x 5 ( x 4 − x ) 1/4 d x is equal to

∫ x 4 ( 1 − x 3 1 ) 1/4 d x put 1 − x 3 1 = t ∴ x 4 dx = 3 dt ∫ 3 t 1/4 d t = 15 4 t 5/4 + C 15 4 ( 1 − x 3 1 ) 5/4 + C

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 min

MathematicsMediumsingle choice

$\int \frac{( x ^{4} - x ) ^{1/4}}{x ^{5}} d x$ is equal to

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Answer:

Solution:

$\int \frac{( 1 - \frac{1}{x ^{3}} ) ^{1/4}}{x ^{4}} d x$ put $1 - \frac{1}{x ^{3}} = t$ $∴ \frac{dx}{x ^{4}} = \frac{dt}{3}$ $\int \frac{t ^{1/4}}{3} d t = \frac{4}{15} t^{5/4} + C$ $\frac{4}{15} (1 - \frac{1}{x ^{3}})^{5/4} + C$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

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