\[ \int \sin ^3(a+b x) \sin ^4(2 a+2 b x) \, dx \]
Optimal antiderivative \[ -\frac {16 \left (\cos ^{5}\left (b x +a \right )\right )}{5 b}+\frac {48 \left (\cos ^{7}\left (b x +a \right )\right )}{7 b}-\frac {16 \left (\cos ^{9}\left (b x +a \right )\right )}{3 b}+\frac {16 \left (\cos ^{11}\left (b x +a \right )\right )}{11 b} \]
command
integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**4,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {472 \sin ^{3}{\left (a + b x \right )} \sin ^{3}{\left (2 a + 2 b x \right )} \cos {\left (2 a + 2 b x \right )}}{1155 b} - \frac {64 \sin ^{3}{\left (a + b x \right )} \sin {\left (2 a + 2 b x \right )} \cos ^{3}{\left (2 a + 2 b x \right )}}{231 b} - \frac {211 \sin ^{2}{\left (a + b x \right )} \sin ^{4}{\left (2 a + 2 b x \right )} \cos {\left (a + b x \right )}}{1155 b} - \frac {304 \sin ^{2}{\left (a + b x \right )} \sin ^{2}{\left (2 a + 2 b x \right )} \cos {\left (a + b x \right )} \cos ^{2}{\left (2 a + 2 b x \right )}}{385 b} - \frac {128 \sin ^{2}{\left (a + b x \right )} \cos {\left (a + b x \right )} \cos ^{4}{\left (2 a + 2 b x \right )}}{231 b} + \frac {272 \sin {\left (a + b x \right )} \sin ^{3}{\left (2 a + 2 b x \right )} \cos ^{2}{\left (a + b x \right )} \cos {\left (2 a + 2 b x \right )}}{1155 b} + \frac {256 \sin {\left (a + b x \right )} \sin {\left (2 a + 2 b x \right )} \cos ^{2}{\left (a + b x \right )} \cos ^{3}{\left (2 a + 2 b x \right )}}{1155 b} - \frac {46 \sin ^{4}{\left (2 a + 2 b x \right )} \cos ^{3}{\left (a + b x \right )}}{165 b} - \frac {192 \sin ^{2}{\left (2 a + 2 b x \right )} \cos ^{3}{\left (a + b x \right )} \cos ^{2}{\left (2 a + 2 b x \right )}}{385 b} - \frac {256 \cos ^{3}{\left (a + b x \right )} \cos ^{4}{\left (2 a + 2 b x \right )}}{1155 b} & \text {for}\: b \neq 0 \\x \sin ^{3}{\left (a \right )} \sin ^{4}{\left (2 a \right )} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________