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$\int x^3sin\left(x\right)dx$
$\int\left(3x^2+1\right)^6dx$
$\int12x^5dx$
$\int xsinx\:dx$
$\int\left(\frac{\cos\left(x\right)}{x}\right)dx$
$\int\left(x^3+2\right)^23x^2dx$
Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.
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