Teaching of integration in H2 Maths
I am an old guy who has retired from teaching (including tuition) but not maths research. Since my field of specialization is mathematical analysis (which contains calculus and S&S), I believe it is worthwhile to mention a possible improvement in the teaching of integration in JCs and MI.
To the best of my knowledge, integration formulas like
int f'(x) (f(x))^n dx=(f(x))^(n+1)/(n+1)+C, int f'(x) e^(f(x)) dx=e^(f(x))+C, int f'(x) cos(f(x)) dx=sin(f(x))+C, ... , int f'(x)/(1+(f(x))^2) dx = tan^(-1) (f(x))+C
only appear in the H2 Maths syllabus after 2010. However, since such formulas can be easily derived via the simple substitution u=f(x), teachers are just making things messy for students. So it is not surprising that certain H2 Maths students cannot integrate 2xe^(x^2) or sin^3 2x cos 2x wrt x.
How can teachers improve their teaching of integration? The first step is to teach differentiation properly!