Question

Find the integral, using techniques from this or the previous chapter. ∫x/√16+8x^2 dx.

Answer 1

$\displaystyle\int\frac x{\sqrt{16+8x^2}}\,\mathrm dx$

Let $u=16+8x^2\implies\mathrm du=16x\,\mathrm dx$. Then the integral becomes

$\displaystyle\frac1{16}\int\frac{\mathrm du}{\sqrt u}\,\mathrm du=\frac18\sqrt u+C$

$=\dfrac18\sqrt{16+8x^2}+C$