Evaluate; \(\int^3_1(3x - 2)^5 dx\)

Explanation

\(\int^3_1(3x - 2)^5 dx\)

Let u = 3x - 2

\(\frac{du}{dx}\) = 3

dx = \(\frac{dy}{3}\)

\(\int^3_1(3x - 2)^5 dx\) = \(\int^7_1 \frac{u^5}{3} du\)

= \(\frac{u^{5 + 1}}{3(5 + 1)}|^7_1\)

= \(\frac{u^5}{18}|^7_1\)

= \(\frac{7^6}{18} = \frac{1^6}{18}\)

= \(\frac{7^6 - 1}{18}\)

= \(\frac{117649}{18}\)

= 6536