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Popular >

integral of (2-1/x)

Solution

\int (2 - \frac{1}{x}) d x

Solution

2 x - ln ∣ x ∣ + C

Solution steps

\int 2 - \frac{1}{x} d x

Apply the Sum Rule:

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

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

\int 2 d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x - ln ∣ x ∣

Add a constant to the solution

= 2 x - ln ∣ x ∣ + C

Popular Examples

integral of x 1 (x)

\int x \frac{d}{1} (x) d x

integral of (xe^x)/(sqrt(e^x-3))

\int \frac{x e ^{x}}{e ^{x} - 3} d x

integral of 1/(1+\sqrt[3]{ax-1)}

integral of (2x)/((x-1)(x+3)^2)

\int \frac{2 x}{( x - 1 ) ( x + 3 ) ^{2}} d x

integral of 2x^2(x+2)^2

\int 2 x^{2} (x + 2)^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of (2-1/x) ?
The integral of (2-1/x) is 2x-ln|x|+C