Expand the expression $15a\left(a+1\right)^3-5a\left(\left(\left(a+1\right)^2\right)^3\right)^2$

$\frac{d}{da}\left(15a\left(a+1\right)^3-5a\left(\left(\left(a+1\right)^2\right)^3\right)^2\right)=15\left(\left(a+1\right)^3+3a\left(a+1\right)^{2}\right)-5\left(\left(a+1\right)^{12}+12a\left(a+1\right)^{11}\right)$ See full solution 

$\int\left(15a\left(a+1\right)^3-5a\left(\left(\left(a+1\right)^2\right)^3\right)^2\right)da=-\frac{15}{4}\left(a+1\right)^{4}+3\left(a+1\right)^{5}+\frac{5}{13}\left(a+1\right)^{13}-\frac{5}{14}\left(a+1\right)^{14}+C_0$ See full solution 