What is the integral of ln(x^2+3) ?

The integral of ln(x^2+3) is xln(x^2+3)+2sqrt(3)arctan(x/(sqrt(3)))-2x+C

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integral of ln(x^2+3)

\int ln (x^{2} + 3) d x

x ln (x^{2} + 3) + 23 arctan (\frac{x}{3}) - 2 x + C

Solution steps

\int ln (x^{2} + 3) d x

Apply Integration By Parts

: x ln (x^{2} + 3) - \int \frac{2 x ^{2}}{x ^{2} + 3} d x

= x ln (x^{2} + 3) - \int \frac{2 x ^{2}}{x ^{2} + 3} d x

\int \frac{2 x ^{2}}{x ^{2} + 3} d x = - 23 arctan (\frac{x}{3}) + 2 x

= x ln (x^{2} + 3) - (- 23 arctan (\frac{x}{3}) + 2 x)

Simplify

= x ln (x^{2} + 3) + 23 arctan (\frac{x}{3}) - 2 x

Add a constant to the solution

= x ln (x^{2} + 3) + 23 arctan (\frac{x}{3}) - 2 x + C

\int \frac{1}{n ln ( n )}

\int_{- 1}^{3} (- x^{3} + 2 x - 11) d x

t^{3} e^{t}

\int x^{2} + 4 x d x

y = \frac{6}{4 - 3 x} - 1, (- 4, 1)

What is the integral of ln(x^2+3) ?
The integral of ln(x^2+3) is xln(x^2+3)+2sqrt(3)arctan(x/(sqrt(3)))-2x+C