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

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

Popular >

integral of log_{2}(x+2)

\int lo g_{2} (x + 2) d x

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

Solution steps

\int lo g_{2} (x + 2) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int_{0}^{1} e^{x} - 1 d x

\int sin (ln (6 x)) d x

\frac{d}{d x} (2 \cdot 3 x)

f (x) = - 4 x + 8

n = 5 \sum \infty \frac{7 ^{n}}{8 ^{n}}

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