\[ \int \frac {\text {ArcTan}(c (a+b x)) \log (d (a+b x))}{a+b x} \, dx \]
Optimal antiderivative \[ \frac {i \ln \left (d \left (b x +a \right )\right ) \polylog \left (2, -i c \left (b x +a \right )\right )}{2 b}-\frac {i \ln \left (d \left (b x +a \right )\right ) \polylog \left (2, i c \left (b x +a \right )\right )}{2 b}-\frac {i \polylog \left (3, -i c \left (b x +a \right )\right )}{2 b}+\frac {i \polylog \left (3, i c \left (b x +a \right )\right )}{2 b} \]
command
int(arctan(c*(b*x+a))*ln(d*(b*x+a))/(b*x+a),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(1087\) |
Maple 2021.1 output
\[ \int \frac {\arctan \left (c \left (b x +a \right )\right ) \ln \left (d \left (b x +a \right )\right )}{b x +a}\, dx \]________________________________________________________________________________________