Answer
What the student did is
$\displaystyle \int f(x)\cdot g(x)dx=\int f(x)dx\cdot\int g(x)dx$,
$(\quad f(x)=4,\quad g(x)=e^{x}-2x\quad)$
which is wrong (the integral of a product is NOT the product of integrals).
Correct answer:$\qquad 4(e^{x}-x^{2})+C$
Work Step by Step
What the student did is
$\displaystyle \int f(x)\cdot g(x)dx=\int f(x)dx\cdot\int g(x)dx$
which is wrong.
$(\quad f(x)=4,\quad g(x)=e^{x}-x^{2}\quad)$
How it should have been done is:
$\displaystyle \int 4(e^{x}-2x)dx=4\int e^{x}dx-4\int 2xdx$
$=4\displaystyle \int e^{x}dx-8\int xdx$
$=4e^{x}-8\displaystyle \cdot\frac{x^{2}}{2}+C$
$=4e^{x}-4x^{2}+C$
$=4(e^{x}-x^{2})+C$
