Find $\displaystyle\displaystyle \displaystyle\int{\frac{x}{{{x}^{2}}+4x+7}}\mathrm{ d}x$.[3] Find

Question

Find $\displaystyle\displaystyle \displaystyle\int{\frac{x}{{{x}^{2}}+4x+7}}\mathrm{ d}x$.[3] Find $\displaystyle\displaystyle\int\limits_{0}^{a}{x\sqrt{a-x}} \;\, \mathrm{ d}x$ by using integration by parts. [4]

Accepted Answer

(a) $\dfrac12\ln(x^2+4x+7)-\dfrac2{\sqrt3}\tan^{-1}\!\left(\dfrac{x+2}{\sqrt3}\right)+C$ (b) $\dfrac4{15}a^{5/2}$

2012 ACJC P1 Q1

2012 ACJC P1 Q1

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