6x-4-4-x-4-2-dx-

Question Number 85441 by jagoll last updated on 22/Mar/20

\int \frac{{6 x}^{4} - 4}{\sqrt{x^{4} - 2}} dx = ?

Answered by john santu last updated on 22/Mar/20

I = \int \frac{4 x^{4}}{\sqrt{x^{4} - 2}} d x = 4 \int x (\frac{x^{3}}{\sqrt{x^{4} - 2}}) d x

= 4 \int \frac{1}{4} x \frac{d (x^{4} - 2)}{\sqrt{x^{4} - 2}}

= 4 (\frac{1}{4} x (2 \sqrt{x^{4} - 2}) - \int \frac{1}{2} \sqrt{x^{4} - 2}) + c

= 2 x \sqrt{x^{4} - 2} - 2 \int \sqrt{x^{4} - 2} d x

J = \int \frac{2 x^{4} - 4}{\sqrt{x^{4} - 2}} d x = 2 \int \frac{x^{4} - 2}{\sqrt{x^{4} - 2}} d x

J = 2 \int \sqrt{x^{4} - 2} d x

t h e a n s w e r

I + J = 2 x \sqrt{x^{4} - 2} - 2 \int \sqrt{x^{4} - 2} d x +

2 \int \sqrt{x^{4} - 2} d x = 2 x \sqrt{x^{4} - 2} + c . ∴

Commented by jagoll last updated on 22/Mar/20

thank you sir

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