Find $\displaystyle\displaystyle \displaystyle\int{x{{\mathrm{e}}^{3{{x}^{2}}+1}}}\mathrm{d}x$.[1]

Question

Find $\displaystyle\displaystyle \displaystyle\int{x{{\mathrm{e}}^{3{{x}^{2}}+1}}}\mathrm{d}x$.[1] Find $\displaystyle\displaystyle \displaystyle\int{{{\sin }^{2}}\left( 5x \right)}\,\mathrm{d}x$.[3] Find $\displaystyle\displaystyle \displaystyle\int{\frac{x}{4{{x}^{2}}-4x+17}}\,\mathrm{d}x$.[5]

Accepted Answer

(a) $\frac{1}{6}{{	ext{e}}^{3{{x}^{2}}+1}}+c$ (b) $\frac{1}{2}x-\frac{1}{20}\sin 10x+c$ (c) $\frac{1}{8}\ln \left| 4{{x}^{2}}-4x+17 ight|+\frac{1}{16}{{	an }^{-1}}\left( \frac{2x-1}{4} ight)+c$

2022 EJC Promo Q6

2022 EJC Promo Q6

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