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Popular >

integral of 2/x+x/2

Solution

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

Solution

2 ln ∣ x ∣ + \frac{x ^{2}}{4} + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 2 ln ∣ x ∣ + \frac{x ^{2}}{4}

Add a constant to the solution

= 2 ln ∣ x ∣ + \frac{x ^{2}}{4} + C

Graph

Popular Examples

integral of (3sec^2(x)-2csc^2(x))

\int (3 sec^{2} (x) - 2 csc^{2} (x)) d x

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

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

integral of ((1-sin^2(x))/(cos(x)))

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

integral of 1/x-1/(x+1)

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

integral of 3/(2\sqrt[3]{(4x-1)^2)}

\int \frac{3}{2 3 ( 4 x - 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of 2/x+x/2 ?
The integral of 2/x+x/2 is 2ln|x|+(x^2)/4+C