What is the integral of-7log_{2}(x) ?

The integral of-7log_{2}(x) is -7(xlog_{2}(x)-1/(ln(2))x)+C

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integral of-7log_{2}(x)

\int - 7 lo g_{2} (x) d x

- 7 (x lo g_{2} (x) - \frac{1}{ln ( 2 )} x) + C

Solution steps

\int - 7 lo g_{2} (x) d x

Take the constant out:

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

= - 7 \cdot \int lo g_{2} (x) d x

Apply Integration By Parts

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

= - 7 (x lo g_{2} (x) - \int \frac{1}{ln ( 2 )} d x)

\int \frac{1}{ln ( 2 )} d x = \frac{1}{ln ( 2 )} x

= - 7 (x lo g_{2} (x) - \frac{1}{ln ( 2 )} x)

Add a constant to the solution

= - 7 (x lo g_{2} (x) - \frac{1}{ln ( 2 )} x) + C

\int e^{x} (x + 1)^{2} d x

y = x^{2} - 4 x, y = 0

23 x^{3} + x^{2} - 12 x + 17

\frac{d y}{d x} = \frac{x - 3}{2 - y}

f (x) = x \cdot ln (x)

What is the integral of-7log_{2}(x) ?
The integral of-7log_{2}(x) is -7(xlog_{2}(x)-1/(ln(2))x)+C