What is the integral of 9ln(x) ?

The integral of 9ln(x) is 9(xln(x)-x)+C

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integral of 9ln(x)

\int 9 ln (x) d x

9 (x ln (x) - x) + C

Solution steps

\int 9 ln (x) d x

Take the constant out:

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

= 9 \cdot \int ln (x) d x

Apply Integration By Parts

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

= 9 (x ln (x) - \int 1 d x)

\int 1 d x = x

= 9 (x ln (x) - x)

Add a constant to the solution

= 9 (x ln (x) - x) + C

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

\frac{\partial}{\partial x} (2 x - x^{3} + 3 x y^{2})

ln (cos (x))

\frac{d y}{d x} = \frac{x}{36 y}

\frac{8}{s ^{2} + 64}