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

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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

\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

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