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∫x 9 ÷(x 2 +4) 6 =?

∫x9÷(x2+4)6=?

Grade:12

1 Answers

jagdish singh singh
173 Points
5 years ago
\hspace{-0.5 cm }$Let $\bf{I = \int\frac{x^9}{(x^2+4)^6}dx = \int\frac{x^9}{x^{12}\cdot \left(1+4x^{-2}\right)^6}dx = \int\frac{x^{-3}}{\left(1+4x^{-2}\right)^6}dx}$\\\\\\ Now put $\bf{1+4x^{-2}=t\;,}$ Then $\bf{x^{-3}dx = -\frac{1}{8}dt\;,}$ So Integral convert into\\\\\\ $\bf{I = -\frac{1}{8}\int \frac{1}{t^6}dt = -\frac{1}{8}\times -\frac{1}{5}\cdot t^{-5}+\mathcal{C} = \frac{1}{40}\cdot \left(\frac{x^2}{x^2+4}\right)^5+\mathcal{C}}$

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