Use a table of integrals to find the indefinite integral $\int \frac { x ^ { 2 } } { ( 8 + 2 x ) ^ { 7 } } d x$ .
A) $\left[ \frac { - 1 } { 4 ( 8 + 2 x ) ^ { 4 } } + \frac { 16 } { 5 ( 8 + 2 x ) ^ { 5 } } - \frac { 64 } { 6 ( 8 + 2 x ) ^ { 6 } } \right] + C$
B) $\frac { 1 } { 8 } \left[ \frac { - 1 } { 4 ( 8 + 2 x ) ^ { 4 } } + \frac { 16 } { 5 ( 8 + 2 x ) ^ { 5 } } - \frac { 64 } { 6 ( 8 + 2 x ) ^ { 6 } } \right] + C$
C) $\frac { 1 } { 8 } \left[ \frac { - 1 } { 4 ( 8 + 2 x ) ^ { 4 } } + \frac { 16 } { 5 ( 8 + 2 x ) ^ { 5 } } + \frac { 64 } { 6 ( 8 + 2 x ) ^ { 6 } } \right] + C$
D) $\frac { 1 } { 8 } \left[ \frac { - 1 } { 4 ( 8 + 2 x ) ^ { 4 } } - \frac { 16 } { 5 ( 8 + 2 x ) ^ { 5 } } + \frac { 64 } { 6 ( 8 + 2 x ) ^ { 6 } } \right] + C$
E) $\left[ \frac { - 1 } { 4 ( 8 + 2 x ) ^ { 4 } } - \frac { 16 } { 5 ( 8 + 2 x ) ^ { 5 } } + \frac { 64 } { 6 ( 8 + 2 x ) ^ { 6 } } \right] + C$

Question

Quizplus · Accepted Answer

The correct answer is obtained by using integration techniques that involve substitution and partial fraction decomposition. The factor of $1/8$ outside the brackets in option B accounts for the $2x$ in the denominator when simplifying the integral, which matches the structure of the given integral.

Use a Table of Integrals to Find the Indefinite Integral ∫x2(8+2x)7dx\int \frac { x ^ { 2 } } { ( 8 + 2 x ) ^ { 7 } } d x∫(8+2x)7x2​dx

Use a Table of Integrals to Find the Indefinite Integral $\int \frac { x ^ { 2 } } { ( 8 + 2 x ) ^ { 7 } } d x$