What is the integral of 5x+1/(2x) ?

The integral of 5x+1/(2x) is (5x^2)/2+1/2 ln|x|+C

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integral of 5x+1/(2x)

\int 5 x + \frac{1}{2 x} d x

\frac{5 x ^{2}}{2} + \frac{1}{2} ln ∣ x ∣ + C

Solution steps

\int 5 x + \frac{1}{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{1}{2 x} d x

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

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

= \frac{5 x ^{2}}{2} + \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= \frac{5 x ^{2}}{2} + \frac{1}{2} ln ∣ x ∣ + C

y = sin (x^{4})

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

g (u) = 2 u + 3 u

- \frac{x}{1 - x ^{2}}

\int 1 + 36 x^{2} d x

What is the integral of 5x+1/(2x) ?
The integral of 5x+1/(2x) is (5x^2)/2+1/2 ln|x|+C