Find $\displaystyle\int{\frac{{{\mathrm{e}}^{\frac{1}{x}}}}{{{x}^{2}}}\,\mathrm{d}x}$, [2] $\display

Question

Find $\displaystyle\int{\frac{{{\mathrm{e}}^{\frac{1}{x}}}}{{{x}^{2}}}\,\mathrm{d}x}$, [2] $\displaystyle\int{\cos kx\cos \left( k+2 ight)x\,\mathrm{d}x}$, where $k$ is a positive constant, [2] $\displaystyle\int{x{{	an }^{-1}}\left( 3x ight)\,\,\mathrm{d}x}$. [6]

Accepted Answer

(a) $-e^{\frac{1}{x}} + C$ (b) $\frac{1}{2}\left[\frac{\sin(2k+1)x}{2k+1} + \sin x\right] + C$ (c) $\frac{1}{2}x^2 \tan^{-1}(3x) - \frac{1}{6}x + \frac{1}{18}\tan^{-1}(3x) + C$

2019 JPJC P1 Q9

2019 JPJC P1 Q9

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