urca3m403

2021-11-20

Evaluate the given integral.
$\int \frac{1+x}{x}dx$

### Answer & Explanation

breisgaoyz

Step 1
we have to evaluate the given integral
$\int \frac{1+x}{x}dx$
Step 2
$\int \frac{1+x}{x}dx$
$=\int \frac{1}{x}dx+\int dx$
$=\mathrm{ln}|x|+x+C$
$\int \frac{1+x}{x}dx=\mathrm{ln}|x|+x+C$

Elizabeth Witte

Step 1: Simplify .
$\int 1+\frac{1}{x}dx$
Step 2: Use Sum Rule: $\int f\left(x\right)+g\left(x\right)dx=\int f\left(x\right)dx+\int g\left(x\right)dx$.
$\int 1dx+\int \frac{1}{x}dx$
Step 3: Use this rule: $\int adx=ax+C$.
$x=\int \frac{1}{x}dx$
Step 4: The derivative of .
$x+\mathrm{ln}x$
Step 5: Add constant.
$x+\mathrm{ln}x+C$

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