/sci/ - Science & Math

Is there a general formula for the antiderivative of x times a function of a quadratic? like [eqn] \int a f(\alpha x^2+\beta x+ \gamma)xdx [/eqn] and the antiderivative of f is F.

I tried this but I could only get it equal to [eqn] \frac {aF(u)}{2\alpha] \pm \frac{a\beta}{8\alpha ^2} \int f(-\frac{1}{4\alpha}v+(\frac{\beta ^2}{4\alpha}-\gamma))v^(-1/2)dv [/eqn]
where [math] u=\alpha x^2+\beta x+ \gamma [/math] and [math] v=\beta^2-4\alpha (\gamma + u)[/math]. There's no +C because there's still an indefinite integral in the expression.

I'm betting it isn't possible to find a formula simpler than the original integral

EE & CS have the biggest normies, its as bad as biology

Most other engineers are also kinda normies

Only chemists i can think of are walter white (based) and that weird guy Gale that got shot (not based) so they cancel

Newton died a virgin for his work, Einstein and Schrodinger were chads, so physics is lowkey hella based