x-2-f-x-3-1-1-x-2-f-1-x-1-x-4x-3-1-x-4-5-0-1-f-x-dx-

Question Number 157655 by tounghoungko last updated on 26/Oct/21

x^{2} f (x^{3}) + \frac{1}{{(1 + x)}^{2}} f (\frac{1 - x}{1 + x}) = 4 x^{3} {(1 + x^{4})}^{5}

\int_{0}^{1} f (x) d x = ?

Commented by cortano last updated on 26/Oct/21

= \frac{65}{3}

Answered by mindispower last updated on 26/Oct/21

\int_{0}^{1} x^{2} f (x^{3}) d x = \frac{1}{3} \int_{0}^{1} f (x) d x

\int_{0}^{1} f (x) d x = 2 \int_{0}^{1} \frac{f (\frac{1 - x}{1 + x})}{{(1 + x)}^{2}} d x