A table of integrals was provided for us in our text-book:
I have two questions in this regard:
1) What would happen to the antiderivatives, F(x), if a constant factor, b, was inserted infront of all all of the functions, f(x)? For instance instead of f(x) = x^n , it would read b* x^n, instead of f(x)= 1/x, it would read f(x)= b* 1/x and so on and so forth.
2) If f(x)= 1/x = x^-1 corresponds to F(x)= lnx + k (where k is a constan term), then what would happen to the formula for F(x), if the numerator (or exponent, depending on which formulation you go by) in f(x) was replaced by a greater or lesser number? I.e. Instead of f(x)= 1/x, it would read 3/x , 0,5/x or -4/x? And same thing if we go by the second formulation that f(x)= x^-1- what if instead of -1, the exponent was -2, 0,3 or 1/5?
Thank you for any help in advance.