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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (log_{2}(x))^2

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

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

Solution steps

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

Apply Integration By Parts

: x lo g_{2} (x)^{2} - \int \frac{2 lo g _{2} ( x )}{ln ( 2 )} d x

= x lo g_{2} (x)^{2} - \int \frac{2 lo g _{2} ( x )}{ln ( 2 )} d x

\int \frac{2 lo g _{2} ( x )}{ln ( 2 )} d x = \frac{2}{ln ^{2} ( 2 )} (x ln (x) - x)

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

Add a constant to the solution

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

\int e^{x} 36 + e^{x} d x

\int \frac{t ^{2} - 9}{t ^{3}} d t

\int (\frac{1}{x ^{\frac{3}{2}}}) d x

\int 0 sin (x) d x

sec^{4} (x)

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