Trig Formulas and Integration Rules

These flashcards cover key integration rules related to trigonometric functions and their inverse, essential for understanding calculus in relation to trigonometry.

Integration Rule: sin(u) du

= -cos(u) + C

Integration Rule: cos(u) du

= sin(u) + C

Integration Rule: e^u du

= e^u + C

Integration Rule: u^n du

= (u^(n+1))/(n+1) + C

Integration Rule: u^(-1) du

= ln|u| + C

Integration of csc²(u) du

= -cot(u) + C

Integration of sec²(u) du

= tan(u) + C

Integration of csc(u) cot(u) du

= -csc(u) + C

Integration of sec(u) tan(u) du

= sec(u) + C

Integration of tan(u) du

= -ln|cos(u)| + C

Integration of cot(u) du

= ln|sin(u)| + C

Integration of sec(u) du

= ln|sec(u) + tan(u)| + C

Integration of csc(u) du

= -ln|csc(u) + cot(u)| + C

Integral du/(a²-u²)^1/2

= arcsin(u/a) + C

Integral du/a²+u²

= 1/a arctan(u/a) + C

Integral du/u(u²-a²)^1/2

= 1/a arcsec(u/a) + C