If e^x ( x+2 x+4 )^2 d x=f(x)+ arbitrary constant, then f(x)=

Step-by-step solution

Given, e^x ( x+2 x+4 )^2 d x=f(x)+ c Now, aligned & e^x ( x+2 x+4 )^2 d x= e^x ( x^2+4+4 x (x+4)^2 ) d x & = e^x ( x x+4 + 4 (x+4)^2 ) d x aligned Let aligned g(x)= & x (x+4)^ , then g^ (x)= 4 (x+4)^2 & = e^x g(x)+g^ (x) d x & =e^x g(x)+c=e^x ( x x+4 )+c aligned f(x)= x e^x x+4