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Popular >

integral of 5x+2/x

Solution

\int 5 x + \frac{2}{x} d x

Solution

\frac{5 x ^{2}}{2} + 2 ln ∣ x ∣ + C

Solution steps

\int 5 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 5 x d x + \int \frac{2}{x} d x

\int 5 x d x = \frac{5 x ^{2}}{2}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{5 x ^{2}}{2} + 2 ln ∣ x ∣

Add a constant to the solution

= \frac{5 x ^{2}}{2} + 2 ln ∣ x ∣ + C

Popular Examples

integral of (x+8)/(x^3+48x-49)

\int \frac{x + 8}{x ^{3} + 48 x - 49} d x

integral of (8z+4z^3-6z^2)

\int (8 z + 4 z^{3} - 6 z^{2}) d z

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

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

integral of y^2sqrt(y+3)

\int y^{2} y + 3 d y

integral of 1/(sqrt(1+p^2))

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

Frequently Asked Questions (FAQ)

What is the integral of 5x+2/x ?
The integral of 5x+2/x is (5x^2)/2+2ln|x|+C