Problem 2

Question

Find the indefinite integral. $$ \int \frac{1}{x-5} d x $$

Step-by-Step Solution

Verified

Answer

The integral of $\frac{1}{x-5}$ dx is \(ln |x - 5| + C.

1Step 1: Identify integral form

Notice the integral is in the form $\int \frac{1}{u} du$, where $u = x - 5$

2Step 2: Apply logarithmic integral rule

By applying the logarithmic integral rule $\int \frac{1}{u} du = ln |u| + C$, the integral becomes: $ln |x - 5| + C$, where $C$ is the constant of integration.

Problem 2

Other exercises in this chapter

Problem 2

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Problem 2

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Problem 2

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of $n .$ Round your answers to four decimal

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Problem 2

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