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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionHard2 minQB

MathematicsHardinteger

If $\int (x^{11} + x^{7} + x^{3}) (2 x^{12} + 3 x^{8} + 6 x^{4})^{1/4} d x = a (2 x^{12} + 3 x^{8} + 6 x^{4})^{5/4} + C$ , find $60 a + 1$ .

Answer:

Solution:

Rewrite the integrand as $(x^{11} + x^{7} + x^{3}) (2 x^{12} + 3 x^{8} + 6 x^{4})^{1/4}$ . The inner derivative is $24 (x^{11} + x^{7} + x^{3})$ , so $a = 1/30$ and $60 a + 1 = 3$ .

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: QB

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