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Chapter 17: Problem 4

Find \(\int 7 x^{-2} \mathrm{~d} x\).

Short Answer

Expert verified
Question: Find the integral of the function \(7x^{-2}\) with respect to x. Answer: The integral of \(7x^{-2}\) with respect to x is \( -7x^{-1} + C\).

Step by step solution

01

Identify the function and its exponent

The given function is \(7x^{-2}\). Here, the exponent is -2.
02

Apply the power rule for integration

Using the power rule, we have: ∫\(7x^{-2}\) dx = \(7\int x^{-2} dx\) Now, by the power rule, we have: \(7\int x^{-2} dx = 7 \cdot \frac{x^{-2 + 1}}{-2 + 1} + C\)
03

Simplify the expression

Now, we will simplify the expression as follows: \(= 7 \cdot \frac{x^{-1}}{-1} + C\) \(= -7x^{-1} + C\)
04

Write the final answer

The integral of \(7x^{-2}\) with respect to x is: \( ∫ 7x^{-2} dx = -7x^{-1} + C\)

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