Use the substitution $u=1-{{x}^{3}}$ to find \(\displaystyle\displaystyle \displaystyle\int{\frac{

Question

Use the substitution $u=1-{{x}^{3}}$ to find $\displaystyle\displaystyle \displaystyle\int{\frac{{{x}^{5}}}{\sqrt{1-{{x}^{3}}}}}\ \mathrm{d}x$.[4] Hence find $\displaystyle\displaystyle \displaystyle\int{\frac{{{x}^{8}}}{\sqrt{1-{{x}^{3}}}}}\ \mathrm{d}x$.[4]

Accepted Answer

(a) $-\dfrac23(1-x^3)^{1/2}+\dfrac29(1-x^3)^{3/2}+C$ (b) $-\dfrac23(1-x^3)^{1/2}+\dfrac49(1-x^3)^{3/2}-\dfrac2{15}(1-x^3)^{5/2}+C$

2023 HCI P2 Q2

2023 HCI P2 Q2

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