\[ \int \frac {\text {Si}\left (d \left (a+b \log \left (c x^n\right )\right )\right )}{x} \, dx \]
Optimal antiderivative \[ \frac {\cos \left (d \left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{b d n}+\frac {\left (a +b \ln \left (c \,x^{n}\right )\right ) \sinIntegral \left (d \left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{b n} \]
command
integrate(sin_integral(d*(a+b*log(c*x^n)))/x,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (b d n \log \left (x\right ) + b d \log \left (c\right ) + a d\right )} \operatorname {Si}\left (b d \log \left (c x^{n}\right ) + a d\right ) + \cos \left (b d n \log \left (x\right ) + b d \log \left (c\right ) + a d\right )}{b d n} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\operatorname {Si}\left (b d \log \left (c x^{n}\right ) + a d\right )}{x}, x\right ) \]