What is the integral of (1+1)/x ?

The integral of (1+1)/x is 2ln|x|+C

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integral of (1+1)/x

integral

\frac{1 + 1}{x}

2 ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (1 + 1) \cdot \int \frac{1}{x} d x

Simplify

= 2 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 ln ∣ x ∣

Add a constant to the solution

= 2 ln ∣ x ∣ + C

\frac{( 3 x ^{2} + 5 )}{( x ^{2} + 1 ) ^{2}}

2 - (\frac{5}{x ^{2}})

1 - x^{2}

∣ x ∣^{4}

\frac{7}{x}