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Question Number 52667 by gunawan last updated on 11/Jan/19

$$\int \frac{x^4+1}{x^2\sqrt{x^4-1}}dx$$

Answered by tanmay.chaudhury50@gmail.com last updated on 11/Jan/19

$$\int \frac{x^2+\frac{1}{x^2}}{\sqrt{x^2(x^2-\frac{1}{x^2})}}dx$$$$\int \frac{x+\frac{1}{x^3}}{\sqrt{x^2-\frac{1}{x^2}}}dx$$$$k^2=x^2-\frac{1}{x^2}$$$$2k\times \frac{dk}{dx}=2x+\frac{2}{x^3}$$$$kdk=(x+\frac{1}{x^3})dx$$$$\int \frac{kdk}{k}$$$$=k+c$$$$=\sqrt{x^2-\frac{1}{x^2}}+c$$

Commented by gunawan last updated on 11/Jan/19

$$\mathrm{thank}\mathrm{you}\mathrm{Sir}$$$$$$

Commented by tanmay.chaudhury50@gmail.com last updated on 11/Jan/19

$$mostwelcome...$$

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