Find f if $\int_0^1 f(x)^2dx=\int_0^1 f(x)^3dx =\int_0^1 f(x)^4dx$
65418
Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$
31768
Roots of a functionwith condition $\int_0^\pi f(x) \sin x dx = \int_0^\pi f(x) \cos x dx =0.$
104145
Finding the value of $3(\alpha-\beta)^2$ if $\int_0^2 f(x)dx=f(\alpha) +f(\beta)$ for all $f$
133851
How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
5180
How to show $\alpha\int_a^cf(x)dx+\beta \int_c^b f(x)dx =0$ means $f(x)=0$ everywhere $?$
112621
Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
122407
If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)dx$
86367
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$
74100
How do you solve $f'(x) = f(f(x))$?
158180
An inequality of $\int_0^1 |f(x)|dx$
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
142682
Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
97643
Prove that:$f(f(x)) = x^2 \implies \int_{0}^{1}{(f(x))^2dx} \geq \frac{3}{13}$
9730
Solve the integral $\int_0^\infty x/(x^3+1) dx$
33989
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
66404
Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$