$f(x) = x + \int_{0}^{1} (xy^2 + x^2y) f(y)dy$. Find $f(x)$
129902
If $f(x)=x+\int_{0}^{1}[xy^2+x^2y]f(y)dy$ where $x$ and$y$ are independent variable.Find $f(x).$
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$
113066
Calculate $\int_0^1f(x)dx$
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
133333
Find $f(x)$ for $f(f(x))=\sin x$
154223
Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
53224
$e^{-x}f(x)=2+ \int_0^x\sqrt{t^4+1}dt$ function for finding the inverse
153942
Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
91333
How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$
10806
Find the value of $\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-(x^2+xy+y^2)} \, dx\,dy$
45787
How can one find the zeroes of $f(x)=ae^{bx}+cx+d$?
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
94869
Show that $ \int_{k}^{2} \frac{1}{f(y)} =1$
53024
$f(x)f(1/x)=f(x)+f(1/x)$
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$