Q.1 (A) (v) ∫ x²(3)^(x^3) dx = _____ A. frac(3)^(x^3)3·log 3+c B. (3)^(x^3)+c C. (log 3)(3)^(x^3)+c D. x²(3)^(x^3)+c

Answer: A. frac(3)^(x^3)3·log 3+c Answer: (a) frac(3)^(x^3)3·log 3+c Put x³=t , so 3x² dx=dt , i.e. x² dx=dt/3 . Then ∫ x² 3^(x^3)dx=1/3∫ 3^t dt=1/3·3^t/log 3+c=frac3^(x^3)3log 3+c .

\(\int x^2(3)^{x^3}\,dx\) = _____

Q.1 (A) (v) \(\int x^2(3)^{x^3}\,dx\) = _____

A. \(\frac{(3)^{x^3}}{3\cdot\log 3}+c\)

B. \((3)^{x^3}+c\)

C. \((\log 3)(3)^{x^3}+c\)

D. \(x^2(3)^{x^3}+c\)

Doubtly Asked 28 Oct 2026 Board exam · June 2026 hsc 12th Save WhatsApp Report

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Answer: A. \(\frac{(3)^{x^3}}{3\cdot\log 3}+c\)

Answer: (a) \(\frac{(3)^{x^3}}{3\cdot\log 3}+c\)

Put \(x^3=t\), so \(3x^2\,dx=dt\), i.e. \(x^2\,dx=\frac{dt}{3}\). Then \(\int x^2 3^{x^3}dx=\frac{1}{3}\int 3^t\,dt=\frac{1}{3}\cdot\frac{3^t}{\log 3}+c=\frac{3^{x^3}}{3\log 3}+c\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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