Use Integration by Parts to Establish a Reduction Formula for the Integral

question 118

Multiple Choice

Use integration by parts to establish a reduction formula for the integral.
- $$\int \mathrm { x } ^ { \mathrm { n } } \mathrm { e } ^ { - a x } \mathrm { dx }$$

• A) \(\int x ^ { n } e ^ { - a x } d x = \frac { x ^ { n } e ^ { - a x } } { a } - \frac { n } { a } \int x ^ { n - 1 } e ^ { - a x } d x\)
• B) \(\int x ^ { n } e ^ { - a x } d x = - a x ^ { n } e ^ { - a x } + n a \int x ^ { n - 1 } e ^ { - a x } d x\)
• C) \(\int x ^ { n } e ^ { - a x } d x = - \frac { x ^ { n } e ^ { - a x } } { a } + \frac { n } { a } \int x ^ { n - 2 } e ^ { - a x } d x\)
• D) \(\int x ^ { n } e ^ { - a x } d x = - \frac { x ^ { n } e ^ { - a x } } { a } + \frac { n } { a } \int x ^ { n - 1 } e ^ { - a x } d x\)

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