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integrate 1/x(x^7+1)??????????????????????????????????????????????????????????????????????????????????????

integrate 1/x(x^7+1)??????????????????????????????????????????????????????????????????????????????????????

Grade:12

1 Answers

jagdish singh singh
173 Points
7 years ago
$\hspace{-0.75 cm}Let $I = \int\frac{1}{x(x^7+1)}dx = \int\frac{1}{x^{8}(1+x^{-7})}dx,$\\\\\\ Now put $1+x^{-7} = t\;,$ Then $-7x^{8}dx = dt\Rightarrow x^{-8}dx = -\frac{1}{7}dt$\\\\\\ So $I = -\frac{1}{7}\int\frac{1}{t}dt = -\frac{1}{7}\ln |t|+\mathcal{C} = -\frac{1}{7}\ln\left|1+x^{-7}\right|+\mathcal{C}$\\\\\\

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