Evaluate \(\int 2(2x – 3)^{\frac{2}{3}} \mathrm d x\)

Explanation

\(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x\)

Let \(u = 2x - 3\)

\(\mathrm d u = 2 \mathrm d x\)

= \(\int u^{\frac{2}{3}} \mathrm d u\)

= \(\frac{u^{\frac{5}{3}}}{\frac{5}{3}} + k\)

= \(\frac{3}{5} (2x - 3)^{\frac{5}{3}} + k\)

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