What is the integral of log_{10}(x^2+4) ?

The integral of log_{10}(x^2+4) is xlog_{10}(x^2+4)-4/(ln(10))(-arctan(x/2)+x/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of log_{10}(x^2+4)

integral

lo g_{10} (x^{2} + 4)

x lo g_{10} (x^{2} + 4) - \frac{4}{ln ( 10 )} (- arctan (\frac{x}{2}) + \frac{x}{2}) + C

Solution steps

\int lo g_{10} (x^{2} + 4) d x

Apply Integration By Parts

: x lo g_{10} (x^{2} + 4) - \int \frac{2 x ^{2}}{ln ( 10 ) ( x ^{2} + 4 )} d x

= x lo g_{10} (x^{2} + 4) - \int \frac{2 x ^{2}}{ln ( 10 ) ( x ^{2} + 4 )} d x

\int \frac{2 x ^{2}}{ln ( 10 ) ( x ^{2} + 4 )} d x = \frac{4}{ln ( 10 )} (- arctan (\frac{x}{2}) + \frac{x}{2})

= x lo g_{10} (x^{2} + 4) - \frac{4}{ln ( 10 )} (- arctan (\frac{x}{2}) + \frac{x}{2})

Add a constant to the solution

= x lo g_{10} (x^{2} + 4) - \frac{4}{ln ( 10 )} (- arctan (\frac{x}{2}) + \frac{x}{2}) + C

ln^{4} (x) + 1

\frac{1}{z ^{2}}

\frac{2 e ^{- x}}{3}

3 - x^{2}

\frac{( x ^{2} + 1 )}{( x + 1 )}

What is the integral of log_{10}(x^2+4) ?
The integral of log_{10}(x^2+4) is xlog_{10}(x^2+4)-4/(ln(10))(-arctan(x/2)+x/2)+C