Find the following integrals: \(\displaystyle\displaystyle \displaystyle\int{\frac{{{\mathrm{e}}^{2x

Question

Find the following integrals: $\displaystyle\displaystyle \displaystyle\int{\frac{{{\mathrm{e}}^{2x}}}{{{\mathrm{e}}^{2x}}-3}\,\,\mathrm{d}x}$[2] $\displaystyle\displaystyle \displaystyle\int{\,\frac{3{{x}^{2}}+2}{\sqrt{\left( {{x}^{3}}+2x-8 \right)}}}\,\mathrm{d}x$.[2] $\int{\frac{1}{{{x}^{2}}+2x+5}\,\,\text{d}x}$ [2] $\int{{{x}^{2}}\ln x\,\,\text{d}x}$[3]

Accepted Answer

(a) $\frac12\ln\lvert e^{2x}-3\rvert+C$; (b) $2\sqrt{x^3+2x-8}+C$; (c) $\frac12\tan^{-1}\left(\frac{x+1}{2}\right)+C$; (d) $\frac{x^3}{3}\ln x-\frac{x^3}{9}+C$.

2018 MJC Promo Q2

2018 MJC Promo Q2

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