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Question Number 171108 by akolade last updated on 08/Jun/22

Answered by qaz last updated on 08/Jun/22

$${\int }_0^1\frac{{\mathrm{x}}^3-{2\mathrm{x}}^4+{\mathrm{x}}^5}{{(\mathrm{x}+1)}^7}\mathrm{dx}={\int }_1^2\frac{{(\mathrm{x}-1)}^3{(\mathrm{x}-2)}^2}{{\mathrm{x}}^7}\mathrm{dx}$$$$={\int }_1^2\frac{{\mathrm{x}}^5-{7\mathrm{x}}^4+{19\mathrm{x}}^3-{25\mathrm{x}}^2+16\mathrm{x}-4}{{\mathrm{x}}^7}\mathrm{dx}$$$$={[-\frac{1}{\mathrm{x}}+\frac{7}{{2\mathrm{x}}^2}-\frac{19}{{3\mathrm{x}}^3}+\frac{25}{{4\mathrm{x}}^4}-\frac{16}{{5\mathrm{x}}^5}+\frac{2}{{3\mathrm{x}}^6}]}_1^2$$$$=\frac{1}{960}$$

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