If-dx-x-3-1-x-6-2-3-xf-x-1-x-6-1-3-C-where-C-is-constant-of-integration-then-find-f-x-

Question Number 208791 by MATHEMATICSAM last updated on 23/Jun/24

If \int \frac{d x}{x^{3} {(1 + x^{6})}^{\frac{2}{3}}} = x f (x) . {(1 + x^{6})}^{\frac{1}{3}} + C

where C is constant of integration then

find f (x) .

Commented by mr W last updated on 23/Jun/24

\int \dots = - \frac{{(1 + x^{6})}^{\frac{1}{3}}}{2 x^{2}} + C

\Rightarrow f (x) = - \frac{1}{2 x^{3}}

Facebook Tweet Pin