1) The general solution to (x^n dx) is [ (x^(n+1)) / (n+1) ] + C. The C is very important because it represents a constant that will differentiate one integral from another.
2)
sin(x) dx = -cos(x) - It is going in reverse (up instead of down) of S,C,-S,-C
cos(x) dx = sin(x) - It is going in reverse (up instead of down) of S,C,-S,-C
sec^2(x) dx = tan(x) - Memorization, since secant is squared I think of tan
sec(x)tan(x) dx = sec(x) - Memorization, since there is a sec and a tan I think of sec
csc^2(x) dx = -cot(x) - Memorization, since co secant is squared I think of a negative co tangent
Integral csc(x)cot(x) dx = -csc(x) - Memorization, since there is a co secant and a co tangent i think of a negative co secant
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