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

$$x^{2}f\left(x^3\right)+\frac{1}{{(1+x)}^2}f\left(\frac{1-x}{1+x}\right)=4x^3{(1+x^4)}^5$$$${\int }_0^{1}f\left(x\right)dx=?$$

Commented by cortano last updated on 26/Oct/21

$$=\frac{65}{3}$$

Answered by mindispower last updated on 26/Oct/21

$${\int }_0^1{x}^{2}f\left(x^3\right)dx=\frac{1}{3}{\int }_0^{1}f\left(x\right)dx$$$${\int }_0^{1}f\left(x\right)dx=2{\int }_0^1\frac{f\left(\frac{1-x}{1+x}\right)}{{(1+x)}^2}dx$$

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