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.

\begin{align}
\int \frac{1}{5}(x^3)-2x+\frac{3}{x}+e^x dx & =  \int \frac{1}{5}x^3 dx- \int 2x dx+ \int \frac{3}{x} dx+ \int e^x dx \\ &= \frac{1}{20}x^4 - x^2 + 3 \ln(x) + e^x + C 
\end{align}
Important rules:
•Derivative of $x^n$ is $\frac{1}{n+1}x^{n+1}$ for $n \neq -1$
•Derivative of $x^{-1}$ is $\ln(x)$
