Chapter 13: Chapter 13

Problem 11

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Evaluate the integrals. $$ \int x^{-5} d x $$

Short Answer

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The short answer for the given integral is: $\int x^{-5} dx = -\frac{1}{4}x^{-4} + C$.

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Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Recognize the format of the integrand

Here, we have an integrand of the form $x^n$ with $n = -5$. The power rule for integration can be applied to this type of function.

Step 2: Apply the power rule for integration

The power rule for integration states that: \[ \int x^n dx = \frac{x^{n+1}}{n+1} + C \] Where $C$ is the constant of integration. In our case, $n = -5$, so we apply the rule as follows: \[ \int x^{-5} dx = \frac{x^{-5+1}}{-5+1} + C = \frac{x^{-4}}{-4} + C \]

Step 3: Write the final answer

Our final answer for this integral is: \[ \int x^{-5} dx = -\frac{1}{4}x^{-4} + C \]

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Chapter 13: Chapter 13

Evaluate the integrals. $$ \int x^{-5} d x $$

Short Answer

Step by step solution

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Step 1: Recognize the format of the integrand

Step 2: Apply the power rule for integration

Step 3: Write the final answer

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More chapters from the book ‘Finite Mathematics and Applied Calculus’

Chapter 0

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 14

Chapter 15

Chapter 16

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