Let f(x)=1+1∫0(xey+yex)f(y)dy where x and y are independent variables. If complete solution set of x for which the function h(x)=f(x)+3x is strictly increasing is (−∞,k), and [.] denotes the greatest integer function, then [43ek] equals to

Let f(x)=1+1∫0(xey+yex)f(y)dy where x and y are independent variable

1.	Let f(x)=1+1∫0(xey+yex)f(y)dy where x and y are independent variables. If complete solution set of x for which the function h(x)=f(x)+3x is strictly increasing is (−∞,k), and [.] denotes the greatest integer function, then [43ek] equals to
Answer» Let $f (x) = 1 + 1 \int 0 (x e^{y} + y e^{x}) f (y) d y$ where $x$ and $y$ are independent variables. If complete solution set of $x$ for which the function $h (x) = f (x) + 3 x$ is strictly increasing is $(- \infty, k),$ and $[.]$ denotes the greatest integer function, then $[\frac{4}{3} e^{k}]$ equals to