What is the integral of-3log_{3}(x) ?

The integral of-3log_{3}(x) is -3(xlog_{3}(x)-1/(ln(3))x)+C

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integral of-3log_{3}(x)

\int - 3 lo g_{3} (x) d x

- 3 (x lo g_{3} (x) - \frac{1}{ln ( 3 )} x) + C

Solution steps

\int - 3 lo g_{3} (x) d x

Take the constant out:

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

= - 3 \cdot \int lo g_{3} (x) d x

Apply Integration By Parts

: x lo g_{3} (x) - \int \frac{1}{ln ( 3 )} d x

= - 3 (x lo g_{3} (x) - \int \frac{1}{ln ( 3 )} d x)

\int \frac{1}{ln ( 3 )} d x = \frac{1}{ln ( 3 )} x

= - 3 (x lo g_{3} (x) - \frac{1}{ln ( 3 )} x)

Add a constant to the solution

= - 3 (x lo g_{3} (x) - \frac{1}{ln ( 3 )} x) + C

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What is the integral of-3log_{3}(x) ?
The integral of-3log_{3}(x) is -3(xlog_{3}(x)-1/(ln(3))x)+C