What is the integral of (ln(x))/(1+x^2) ?

The integral of (ln(x))/(1+x^2) is ln(x)arctan(x)-1/2 i(\Li_{2}(-ix)-\Li_{2}(ix))+C

Popular >

integral of (ln(x))/(1+x^2)

\int \frac{ln ( x )}{1 + x ^{2}} d x

ln (x) arctan (x) - \frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x)) + C

Solution steps

\int \frac{ln ( x )}{1 + x ^{2}} d x

Apply Integration By Parts

: ln (x) arctan (x) - \int \frac{arctan ( x )}{x} d x

= ln (x) arctan (x) - \int \frac{arctan ( x )}{x} d x

\int \frac{arctan ( x )}{x} d x = \frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x))

= ln (x) arctan (x) - \frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x))

Add a constant to the solution

= ln (x) arctan (x) - \frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x)) + C

\int ln (\frac{x}{x + 2}) d x

\frac{d}{d x} (x^{5} - 4 x^{3} + x - 1)

24 y^{^{'''}} + 2 y^{^{''}} - 5 y^{^{'}} - y = 0

\int - cos^{4} (x) d x

f (x) = 6 x^{2} - 4 x + 5

What is the integral of (ln(x))/(1+x^2) ?
The integral of (ln(x))/(1+x^2) is ln(x)arctan(x)-1/2 i(\Li_{2}(-ix)-\Li_{2}(ix))+C