Porisma

A hint to get started

Expand or match the inner derivative

Integrate with respect to xx: (a) x(1−x)\sqrt{x}(1-x); (b) (x1/2+3)2(x^{1/2}+3)^2; (c) (5x+4)5(5x+4)^5; (d) x(2x2−3)4x(2x^2-3)^4; (e) 2x+3(x2+3x)3\frac{2x+3}{(x^2+3x)^3}.

CJC · Lecture · Example 2

Expand simple products and squares when the inner derivative does not match.

Teacher scaffold: name f and its derivative first; look for the derivative or supply it when only a nonzero constant factor is missing.

Read the worked solution