What's the integral of x^2 +3/x, with respect to x?
A: x3/3 + 3ln(x) + A.
Step-by-step solution:
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.
