<s>[INST] Indefinite Integral of a function $$\int \left(\frac15 x^3 - 2x + \frac3x + e^x \right ) \mathrm dx$$
I came up with
$$F=x^4-x^2+\frac{3x}{\frac12 x^2}+e^x$$
but that was wrong.
 [/INST] $\int cx^n=c\int x^n=c\frac{x^{n+1}}{n+1}$ when $n\neq -1$
Thus, $\int \frac{1}{5}x^3=\frac{1}{20}x^4$
Also, by the same rule, $\int -2x=-x^2$
$\int \frac{1}{x}=\ln(x)$
Thus, $\int \frac{3}{x}=3\ln(x)$
$\int e^x=e^x$
Thus, by above, the required integral is 
$F(x)=\frac{1}{20}x^4-x^2+3\ln(x)+e^x+c$
Done.
</s>