\[ \int \frac {(h+i x)^4}{(d e+d f x) (a+b \log (c (e+f x)))} \, dx \]
Optimal antiderivative \[ \frac {4 i \left (-e i +f h \right )^{3} \expIntegral \left (\frac {a +b \ln \left (c \left (f x +e \right )\right )}{b}\right ) {\mathrm e}^{-\frac {a}{b}}}{b c d \,f^{5}}+\frac {6 i^{2} \left (-e i +f h \right )^{2} \expIntegral \left (\frac {2 a +2 b \ln \left (c \left (f x +e \right )\right )}{b}\right ) {\mathrm e}^{-\frac {2 a}{b}}}{b \,c^{2} d \,f^{5}}+\frac {4 i^{3} \left (-e i +f h \right ) \expIntegral \left (\frac {3 a +3 b \ln \left (c \left (f x +e \right )\right )}{b}\right ) {\mathrm e}^{-\frac {3 a}{b}}}{b \,c^{3} d \,f^{5}}+\frac {i^{4} \expIntegral \left (\frac {4 a +4 b \ln \left (c \left (f x +e \right )\right )}{b}\right ) {\mathrm e}^{-\frac {4 a}{b}}}{b \,c^{4} d \,f^{5}}+\frac {\left (-e i +f h \right )^{4} \ln \left (a +b \ln \left (c \left (f x +e \right )\right )\right )}{b d \,f^{5}} \]
command
int((i*x+h)^4/(d*f*x+d*e)/(a+b*ln(c*(f*x+e))),x,method=_RETURNVERBOSE)
Maple 2022.1 output
\[ \text {output too large to display} \]
Maple 2021.1 output \[ \int \frac {\left (i x +h \right )^{4}}{\left (d f x +d e \right ) \left (b \ln \left (\left (f x +e \right ) c \right )+a \right )}\, dx \]____________________________________________________________________