What is the integral of (ln(x^3))/(-804x^2) ?

The integral of (ln(x^3))/(-804x^2) is -(-ln(x)-1)/(268x)+C

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integral of (ln(x^3))/(-804x^2)

\int \frac{ln ( x ^{3} )}{- 804 x ^{2}} d x

- \frac{- ln ( x ) - 1}{268 x} + C

Solution steps

\int \frac{ln ( x ^{3} )}{- 804 x ^{2}} d x

Take the constant out:

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

= \frac{1}{- 804} \cdot \int \frac{ln ( x ^{3} )}{x ^{2}} d x

Simplify

= (- \frac{1}{804}) \cdot \int \frac{ln ( x ^{3} )}{x ^{2}} d x

Simplify

ln (x^{3}) : 3 ln (x)

= (- \frac{1}{804}) \cdot \int \frac{3 ln ( x )}{x ^{2}} d x

Take the constant out:

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

= (- \frac{1}{804}) \cdot 3 \cdot \int \frac{ln ( x )}{x ^{2}} d x

Apply Integration By Parts

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

= (- \frac{1}{804}) \cdot 3 (- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x)

\int - \frac{1}{x ^{2}} d x = \frac{1}{x}

= (- \frac{1}{804}) \cdot 3 (- \frac{ln ( x )}{x} - \frac{1}{x})

Simplify

(- \frac{1}{804}) \cdot 3 (- \frac{ln ( x )}{x} - \frac{1}{x}) : - \frac{- ln ( x ) - 1}{268 x}

= - \frac{- ln ( x ) - 1}{268 x}

Add a constant to the solution

= - \frac{- ln ( x ) - 1}{268 x} + C

(0.3, - 1), (- 0.1, - 0.8)

\frac{\partial}{\partial x} (8 e^{x})

\frac{d}{d x} ((x^{3} - 2 x + 1) (2 x^{2} + 3 x))

f (x) = \frac{x - 6}{9 x - 1}, at x = 1

What is the integral of (ln(x^3))/(-804x^2) ?
The integral of (ln(x^3))/(-804x^2) is -(-ln(x)-1)/(268x)+C