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)