Grade 12Integral Calculus

∫x⁹÷(x²+4)⁶=?

UTKARSH CHOUHAN

10 Years agoGrade 12

1 Answer

jagdish singh singh

10 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}}$$