What is the integral of-4log_{7}(x) ?

The integral of-4log_{7}(x) is -4(xlog_{7}(x)-1/(ln(7))x)+C

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integral of-4log_{7}(x)

\int - 4 lo g_{7} (x) d x

- 4 (x lo g_{7} (x) - \frac{1}{ln ( 7 )} x) + C

Solution steps

\int - 4 lo g_{7} (x) d x

Take the constant out:

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

= - 4 \cdot \int lo g_{7} (x) d x

Apply Integration By Parts

: x lo g_{7} (x) - \int \frac{1}{ln ( 7 )} d x

= - 4 (x lo g_{7} (x) - \int \frac{1}{ln ( 7 )} d x)

\int \frac{1}{ln ( 7 )} d x = \frac{1}{ln ( 7 )} x

= - 4 (x lo g_{7} (x) - \frac{1}{ln ( 7 )} x)

Add a constant to the solution

= - 4 (x lo g_{7} (x) - \frac{1}{ln ( 7 )} x) + C

\int x^{2} - 7 x d x

\int (3 sin (x)) d x

f (x) = \frac{x + 7}{x}

n = 1 \sum \infty \frac{1}{3 ^{n - 3}}

y = \frac{2 x + 1}{x + 2}, (1, 1)

What is the integral of-4log_{7}(x) ?
The integral of-4log_{7}(x) is -4(xlog_{7}(x)-1/(ln(7))x)+C