What is the integral of (xln(2)+3/(2x)) ?

The integral of (xln(2)+3/(2x)) is 1/2 ln(2)x^2+3/2 ln|x|+C

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integral of (xln(2)+3/(2x))

\int (x ln (2) + \frac{3}{2 x}) d x

\frac{1}{2} ln (2) x^{2} + \frac{3}{2} ln ∣ x ∣ + C

Solution steps

\int x ln (2) + \frac{3}{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 ln (2) d x + \int \frac{3}{2 x} d x

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

\int \frac{3}{2 x} d x = \frac{3}{2} ln ∣ x ∣

= \frac{1}{2} ln (2) x^{2} + \frac{3}{2} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{2} ln (2) x^{2} + \frac{3}{2} ln ∣ x ∣ + C

f (x) = x - 6

f (x) = 3 e^{2 x^{2}}

\int_{- 2}^{0} (5 x^{2} + 5 x) d x

x \to \infty lim (5 x^{3})

\frac{d}{d x} (\frac{2 x + 1}{x - 1})

What is the integral of (xln(2)+3/(2x)) ?
The integral of (xln(2)+3/(2x)) is 1/2 ln(2)x^2+3/2 ln|x|+C