What is the integral of ln(x/2) ?

The integral of ln(x/2) is xln(x/2)-x+C

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integral of ln(x/2)

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

x ln (\frac{x}{2}) - x + C

Solution steps

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

Apply Integration By Parts

: x ln (\frac{x}{2}) - \int 1 d x

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

\int 1 d x = x

= x ln (\frac{x}{2}) - x

Add a constant to the solution

= x ln (\frac{x}{2}) - x + C

\int x e^{3 x + 1} d x

y = 4 x^{2}, y = 4

x \to 2 lim (- x^{2} + 4 x - 2)

\int \frac{9 x ^{3}}{x ^{2} + 1} d x

\int \frac{2 x - 3}{x ^{2} + 6 x + 4} d x