To evaluate

$$cos$5($x$)$sin$4($x$)$dx$,$cos$5($x$)$sin$4($x$)$dx$,$

one first makes the substitution$$uu$=.$

This reduces the problem to integrating the$$polynomial P$($u$)$P$($u$)=.$

The general antiderivative $$P$($u$)$du$$P$($u$)$du$=.$

In terms of the original variable xx$,$

this antiderivative can be expressed as $.$

Your last answer was interpreted as follows:

sin$($x$)$sin$($x$)$

The variables found in your answer were: $[$x$][$x$]$

Your last answer was interpreted as follows:

u$4+2$u$6+$u$8$u$4+2$u$6+$u$8$

The variables found in your answer were: $[$u$][$u$]$

Your last answer was interpreted as follows:

u$552$u$77+$u$99+$Cu$552$u$77+$u$99+$C

The variables found in your answer were: $[$C$,$u$][$C$,$u$]$

Your last answer was interpreted as follows:

sin$5($x$)52$sin$7($x$)7+$sin$9($x$)9+$Csin$5($x$)52$sin$7($x$)7+$sin$9($x$)9+$C

The variables found in your answer were: $[$C$,$x$][$C$,$x$]$