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

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

  • A.
    3/5(2x-3)5/3 + k
  • B.
    6/5(2x-3)5/3 + k
  • C.
    2x-3+k
  • D.
    2(2x-3)+k
Correct Answer: Option A
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)