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A: x3/3 + 3ln(x) + A.
Integral (x2+3/x dx) =
[as integrals preserve sums]
integral (x2 dx) + integral (3/x dx) =
[raise exponent by one, multiply by the reciprocal, add a constant]
x3/3 + C + integral (3/x dx) =
[3 is a constant, so we we can take it out of the integral. The anti-derivative of 1/x dx is ln(x)+D, which is a standard result you need to know]
x3/3 + C + 3(ln(x) + D)=
[merge the constants into one constant]
x3/3 + 3ln(x) + A.see more
If we apply a function and then its inverse, we should get back to where we started.
Suppose we start with an element x. If we apply f to it, we get to x+2. In order to get back to where we started (i.e. x), we need to subtract 2.
Hence, the inverse of the function f is