What is the integral of 0.5ln(x) ?

The integral of 0.5ln(x) is 0.5(xln(x)-x)+C

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integral of 0.5ln(x)

\int 0.5 ln (x) d x

0.5 (x ln (x) - x) + C

Solution steps

\int 0.5 ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 0.5 \cdot \int ln (x) d x

Apply Integration By Parts

: x ln (x) - \int 1 d x

= 0.5 (x ln (x) - \int 1 d x)

\int 1 d x = x

= 0.5 (x ln (x) - x)

Add a constant to the solution

= 0.5 (x ln (x) - x) + C

x \to 1 lim (x^{2} + 4 x + 3)

\int_{0}^{4} x - \frac{x}{2} d x

4 s - 1

f (x) = 2 x^{2} + 4 x, (- 3, 6)

x \to 1 lim (ln (x^{5} - 1))