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Popular >

integral of x+2/x

Solution

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

Solution

\frac{x ^{2}}{2} + 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{2}}{2} + 2 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + 2 ln ∣ x ∣ + C

Popular Examples

integral of (3x^4-9x^2+1)/(x^2)

\int \frac{3 x ^{4} - 9 x ^{2} + 1}{x ^{2}} d x

integral of 3e^x+4

\int 3 e^{x} + 4 d x

integral of 1/(sin^2(y)csc(y))

\int \frac{1}{sin ^{2} ( y ) csc ( y )} d y

integral of (2x+1)*cos(4x)

\int (2 x + 1) \cdot cos (4 x) d x

integral of (5x^2+14x+10)/((x+2)(x+1)^2)

\int \frac{5 x ^{2} + 14 x + 10}{( x + 2 ) ( x + 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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