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Question Number 131058 by pipin last updated on 01/Feb/21

$$\int \frac{({\mathrm{x}}^2+2)({\mathrm{x}}^2+3)({\mathrm{x}}^2+4)}{({\mathrm{x}}^2+5)({\mathrm{x}}^2+6)({\mathrm{x}}^2+7)}\mathrm{dx}$$

Answered by MJS_new last updated on 01/Feb/21

$$=\int 1-\frac{3}{x^2+5}+\frac{24}{x^2+6}-\frac{30}{x^2+7}dx=$$$$=x-\frac{3\sqrt{5}}{5}\arctan \frac{\sqrt{5}x}{5}+4\sqrt{6}\arctan \frac{\sqrt{6}x}{6}-\frac{30\sqrt{7}}{7}\arctan \frac{\sqrt{7}x}{7}+C$$

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