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

= 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

\int (2 x + y) d x

f (x) = arctan (x^{4})

\int \frac{3}{x ^{2} + 1} d x

\int sec^{4} (3 x) tan^{4} (3 x) d x

y^{^{'}} + \frac{7}{x + 3} y = (x + 3)^{3}

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