What is the integral of 13log_{15}(x) ?

The integral of 13log_{15}(x) is 13(xlog_{15}(x)-1/(ln(15))x)+C

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integral of 13log_{15}(x)

\int 13 lo g_{15} (x) d x

13 (x lo g_{15} (x) - \frac{1}{ln ( 15 )} x) + C

Solution steps

\int 13 lo g_{15} (x) d x

Take the constant out:

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

= 13 \cdot \int lo g_{15} (x) d x

Apply Integration By Parts

= 13 (x lo g_{15} (x) - \int \frac{1}{ln ( 15 )} d x)

\int \frac{1}{ln ( 15 )} d x = \frac{1}{ln ( 15 )} x

= 13 (x lo g_{15} (x) - \frac{1}{ln ( 15 )} x)

Add a constant to the solution

= 13 (x lo g_{15} (x) - \frac{1}{ln ( 15 )} x) + C

What is the integral of 13log_{15}(x) ?
The integral of 13log_{15}(x) is 13(xlog_{15}(x)-1/(ln(15))x)+C