Show that \(\dfrac{\mathrm{d}}{\mathrm{d}x}\left[(x^2+x+1)\sqrt[3]{x+1}\right]=\dfrac{7x^2+10x+

Question

Show that $\dfrac{\mathrm{d}}{\mathrm{d}x}\left[(x^2+x+1)\sqrt[3]{x+1}\right]=\dfrac{7x^2+10x+4}{3(x+1)^{2/3}}$.[4] Hence evaluate $\displaystyle\int_0^7\dfrac{7x^2+10x+4}{3(x+1)^{2/3}}\,\mathrm{d}x$.[3]

Accepted Answer

$113$

Polynomial factor with a cube root

Polynomial factor with a cube root

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