$\int\:\:x\sqrt{1+x^2}dx$
$\int x\sqrt[3]{3-x^2}dx$
$\int\sqrt{1\:-\:x^2}dx$
$\int\sqrt{1-7w^2}dw$
$\int x^2\sqrt{x^2-4}dx$
$\int2x\sqrt{x^2+1}dx$
$\int\sqrt{5x+3}dx$
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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