Key to "Evaluate the integral. ∫3xdx"

deliredejoker7m

Answered question

2021-11-20

Evaluate the integral.

\int \frac{3}{x} d x

Zachary Pickett

Beginner2021-11-21Added 17 answers

Step 1
the given integral is:

\int \frac{3}{x} d x

we have to evaluate the given integral.
let the given integral be I.
therefore,

I = \int \frac{3}{x} d x

Step 2

I = \int \frac{3}{x} d x

= 3 \int \frac{d x}{x}

= 3 \ln | x | + C

(because

\int \frac{d x}{x} = \ln | x |

)
where C is the constant of integration.
therefore,

I = \int \frac{3}{x} d x = 3 \ln | x | + C

therefore the value of the given integral

\int \frac{3}{x} d x i s 3 \ln | x | + C

Todd Williams

Beginner2021-11-22Added 18 answers

Step 1: Use Constant Factor Rule:

\int c f (x) d x = c \int f (x) d x

3 \int \frac{1}{x} d x

Step 2: The derivative of

\ln x i s \frac{1}{x}

3 \ln x

Step 3: Add constant.

3 \ln x + C

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