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integration (x^2 - 1)/x^3 root(2x^4 - 2x^2 + 1) integration question solve these

integration (x^2 - 1)/x^3 root(2x^4 - 2x^2 + 1) integration question solve these

Grade:12

1 Answers

jagdish singh singh
173 Points
4 years ago
\hspace{-0.6 cm}I = \int\frac{x^2-1}{x^3\sqrt{2x^4-2x^2+1}}dx = \int\frac{x^2-1}{x^3\cdot x^2\sqrt{2-2x^{-2}+x^{-4}}}dx$\\\\\\$=\int\frac{x^{-3}-x^{-5}}{\sqrt{2-2x^{-2}+x^{-4}}}dx\;,$ Put $2-2x^{-2}+x^{-4} = t^2\;,$ \\\\\\$\Rightarrow 4(x^{-3}-x^{-5})dx=2tdt\;,$ So $I = \frac{1}{2}\int\frac{t}{t}dt=\frac{1}{2}t+\mathcal{C}$

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