Show that \(\dfrac{\mathrm{d}}{\mathrm{d}x}\left[(x^2-2x+3)\sqrt{2x+1}\right]=\dfrac{5x^2-4x+1}

Question

Show that $\dfrac{\mathrm{d}}{\mathrm{d}x}\left[(x^2-2x+3)\sqrt{2x+1}\right]=\dfrac{5x^2-4x+1}{\sqrt{2x+1}}$.[4] Hence evaluate $\displaystyle\int_0^4\dfrac{5x^2-4x+1}{\sqrt{2x+1}}\,\mathrm{d}x$.[3]

Accepted Answer

$30$

Quadratic factor with a square root

Quadratic factor with a square root

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