What is $f(x) = int xe^x$ if $f(2)=3$ ?

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Answer 1 · 2018-03-05T15:08:46

$f(x)=xe^x-e^x+3-e^2$

$f(x)=intxe^xdx, f(2)=3$

$f(x)=intu(dv)/(dx)dx=uv-intv(du)/(dx)dx$

in this case

$u=x=>(du)/(dx)=1$

$(dv)/(dx)=e^x=>v=e^x$

$:.f(x)=xe^x-inte^xdx$

$f(x)=xe^x-e^x+c$

$f(2)=3$

$:. f(2)=3=2e^2-e^2+c$

$c=3-e^2$

$f(x)=xe^x-e^x+3-e^2$

What is f(x) = int xe^xf(x) = int xe^x if f(2)=3 f(2)=3 ?