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Integral f (x^3 + x)^5 (3x^2 + 1)dx will be _____?

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Integral f (x^3 + x)^5 (3x^2 + 1)dx will be _____? Answer: (x^3 + x)^6/6 + C

u=x3+x dx/du =3x2+1⇒du=(3x2+1)dx ∫(x3+x)5(3x2+1)dx=∫u5du ∫u5du=6u6 +C 6/(x3+x)6 +C (x3+x)66+C\boxed{\dfrac{(x^3 + x)^6}{6} + C}6(x3+x)6 +C

Question context

This question is part of 📏 Arithmetic Aptitude within the broader 🧠 Aptitude Mastery subject and appears in the SPSC – Sindh Public Service Commission preparation collection. Reviewing the answer together with nearby questions helps reinforce the underlying concept and identify how it may appear in competitive exams.