If $\int \frac{x^3}{\sqrt{1 + x^2}} \, dx = a(1 + x^2)\sqrt{1 + x^2} + b\sqrt{1 + x^2} + c$ (where $c$ is a constant of integration), then the value of $3ab$ is
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Calculus Tip: When an integrand contains an algebraic square root like $\sqrt{cx^2+d}$ and an odd power of $x$ outside, substituting the expression inside the root for $t^2$ (not just $t$) eliminates fractional powers and makes integration drastically simpler.