Question

Find the integral:

[ ∫ 15x⁻⁸ dx ]
A. (105/x)⁷ + C
B. (15/(7x))⁹ + C
C. -120x⁻⁹ + C
D. -(15/7)x⁻⁷ + C

Answer 1

The integral of 15x^(-8) using basic integration rules is -(15/7)x^(-7) + C, which corresponds to option D.

Step-by-step explanation:

The integral of a given function can be solved through basic integration rules. The integral given is ∫ 15x⁻⁸ dx. When integrating a power of x, we use the rule ∫ x^n dx = x^(n+1) / (n+1) + C, where n is not equal to -1. Using this rule, we increment the power by 1 and divide by the new power. Therefore, the integral of 15x⁻⁸ is -15x⁻⁷ / (-7) + C, which simplifies to -(15/7)x⁻⁷ + C. This matches option D: -(15/7)x⁻⁷ + C.