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

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

\frac{\partial}{\partial y} (- 6 x y - x^{6} - y^{6})

\frac{( 4 x + 3 ) ^{8}}{( x ) ^{4}}

x \to 0 lim (\frac{6}{1 + x})

\frac{\partial}{\partial x} (e^{5 x + 3 y})

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