integeral general rules and notes

Question 1

1/(sin^m x . cos^n x)

Answer 1

if m+n even, then divide by cos^(m+n)x

Question 2

1/sin(x-a)sin(x-b)

Answer 2

multiply divide by sin(b-a)

Question 3

when power 2 for sin / cos in denominator

Answer 3

divide by cos/sin square

Question 4

in form x^2 + a/ x^4 + x^2 = c

Answer 4

divide by x^2

Question 5

in questions where numerator is sinx +- cosx

Answer 5

let t = integral of numerator

Question 6

L/Q, LrootQ, L/rootQ

Answer 6

L = A dQ + B

Question 7

by parts

Answer 7

∫ u * v dx = u ∫ v − ∫[du ∫v]

Question 8

∫e^(g(x)) [f(x) g’(x) + f’(x)]

Answer 8

e^(g(x)) f(x)