"Evaluate the given integral. ∫1+xxdx" was answered by our community

urca3m403

Answered question

2021-11-20

Evaluate the given integral.

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

breisgaoyz

Beginner2021-11-21Added 14 answers

Step 1
we have to evaluate the given integral

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

Step 2

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

= \int \frac{1}{x} d x + \int d x

= \ln | x | + x + C

\int \frac{1 + x}{x} d x = \ln | x | + x + C

Elizabeth Witte

Beginner2021-11-22Added 24 answers

Step 1: Simplify

\frac{1 + x}{x} \to 1 + \frac{1}{x}

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

Step 2: Use Sum Rule:

\int f (x) + g (x) d x = \int f (x) d x + \int g (x) d x

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

Step 3: Use this rule:

\int a d x = a x + C

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

Step 4: The derivative of

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

x + \ln x

Step 5: Add constant.

x + \ln x + C

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