What is the integral of 8ln(x) ?

The integral of 8ln(x) is 8(xln(x)-x)+C

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integral of 8ln(x)

\int 8 ln (x) d x

8 (x ln (x) - x) + C

Solution steps

\int 8 ln (x) d x

Take the constant out:

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

= 8 \cdot \int ln (x) d x

Apply Integration By Parts

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

= 8 (x ln (x) - \int 1 d x)

\int 1 d x = x

= 8 (x ln (x) - x)

Add a constant to the solution

= 8 (x ln (x) - x) + C

\frac{d}{d x} (x^{8} ln (9 x))

y^{^{'}} + 2 y = 3, y (0) = 0

\frac{d}{d x} (4^{s i n^{2} (x) + c o s (3 x)})

2 ln (x) + 6