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Popular Calculus >

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

Graph

Popular Examples

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

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

integral of x+C

\int x + C d x

integral of 5xcos(nx)

\int 5 x cos (n x) d x

integral of tan^3((2x)/a)

\int tan^{3} (\frac{2 x}{a}) d x

integral of (9x^2+4x+1)e^{3x^3+2x^2+x}

\int (9 x^{2} + 4 x + 1) e^{3 x^{3} + 2 x^{2} + x} 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