Evaluate $\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x$ .
A) $\frac { 49 } { 9 } \left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$
B) $\frac { x ^ { 2 } } { 14 } - 2 x + C$
C) $\frac { 7 } { 9 } \left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$
D) $\left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$

Question

Quizplus · Accepted Answer

To integrate $\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x$, use the substitution $u = \frac{x}{7} - 2$, then apply the power rule for integration, $\int u^n du = \frac{u^{n+1}}{n+1} + C$, with $n = \frac{2}{7}$, resulting in $\frac{49}{9}\left(\frac{x}{7} - 2\right)^{\frac{9}{7}} + C$.

Evaluate ∫(x7−2)2/7dx\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x∫(7x​−2)2/7dx

Evaluate $\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x$