What is the integral of ln(4+x^2) ?

The integral of ln(4+x^2) is xln(4+x^2)-4(-arctan(x/2)+x/2)+C

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integral of ln(4+x^2)

\int ln (4 + x^{2}) d x

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

Solution steps

\int ln (4 + x^{2}) d x

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

What is the integral of ln(4+x^2) ?
The integral of ln(4+x^2) is xln(4+x^2)-4(-arctan(x/2)+x/2)+C