Integration problem.someone plzzzzzzzzzzzzzzz help

Integrate:
1) [(x-1)√x4+2x3-x2+2x+1]/x2(x+1)
2) (x2-1)/(x32x4-2x2+1)

5 Answers

1708
man111 singh ·

\hspace{-16}$\;\bf{(2)}$\;\;\; $Given $\bf{\int\frac{\left(x^2-1\right)}{x^3\sqrt{2x^4-2x^2+1}}dx}$\\\\\\ We can write it as $\bf{\int\frac{(x^2-1)}{x^3\cdot x^2\sqrt{2-2x^{-2}+x^{-4}}}dx}$\\\\\\ We can Write it as $\bf{\int\frac{(x^{-3}-x^{-5})}{\sqrt{2-2x^{-2}+x^{-4}}}dx}$\\\\\\ Now Let $\bf{\left(2-2x^{-2}+x^{-4}\right)=t^2\;,}$ Then $\bf{\left(x^{-3}-x^{-5}\right)dx = \frac{t}{2}dt}$\\\\\\ So Integral is $\bf{=\frac{1}{2}\int\frac{t}{t}dt = \frac{1}{2}\sqrt{2-2x^{-2}+x^{-4}}+\mathbb{C}}$

146
Amartya Kumar Mistry ·

for the second question take x^4 common from deno. and then after substitution proceed

1357
Manish Shankar ·

in the first take x+1/x + 1 as t

263
Sushovan Halder ·

sir after that it is coming (√y2-4)/(y+1)

1357
Manish Shankar ·

y=2secθ may help

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