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Popular >

integral of 2/x+1

Solution

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

Solution

2 ln ∣ x ∣ + x + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 1 d x = x

= 2 ln ∣ x ∣ + x

Add a constant to the solution

= 2 ln ∣ x ∣ + x + C

Popular Examples

integral of (2x-3y+1)

\int (2 x - 3 y + 1) d x

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

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

integral of 20e^{-5x}

\int 20 e^{- 5 x} d x

integral of (sqrt(3x+5))/x

\int \frac{3 x + 5}{x} d x

integral of x+C

\int x + C d x

Frequently Asked Questions (FAQ)

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