Solve the integral 2 on top and 1 on the bottom.

Question

₁²∫x²/x³+1 dx

Answer 1

This is assuming that there should have been parentheses around (x^3+1).

Answer 2

Assuming you've written the problem correctly, the integrand can be rewritten as:

f(x) = x^(-1) + 1

An antiderivative of this is:

F(x) = ln|x| + x

Thus the value of the definite integral is:

F(2) - F(1) = [ln|2| + 2] - [ln|1| + 1] = ln(2) + 1

HOWEVER, I suspect that you are missing some parentheses, and the actual integral was supposed to be:

x^2/(x^3 + 1)

If this is the case, the u-substitution u = x^3 +1 will work very easily.