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

The integral of xln(2)+3/2 x is 1/2 ln(2)x^2+(3x^2)/4+C

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integral of xln(2)+3/2 x

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

\frac{1}{2} ln (2) x^{2} + \frac{3 x ^{2}}{4} + 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 x ^{2}}{4}

= \frac{1}{2} ln (2) x^{2} + \frac{3 x ^{2}}{4}

Add a constant to the solution

= \frac{1}{2} ln (2) x^{2} + \frac{3 x ^{2}}{4} + C

x y^{^{'}} + 2 y = 4 sin (x)

\frac{d}{d x} (x^{2} + 8 x)

\frac{\partial}{\partial x} (x e^{- 2 x})

(3 x - 2 x^{2})^{3}

x \to - 1 lim (\frac{x ^{3}}{x ^{2} - 1})

What is the integral of xln(2)+3/2 x ?
The integral of xln(2)+3/2 x is 1/2 ln(2)x^2+(3x^2)/4+C