Integration (solve)

X^-3(x+1)dx

To solve this integral, we first need to simplify the expression by expanding the term (x+1) with X^-3.

X^-3(x+1) = X^-3 * x + X^-3 * 1
= X^-2 + X^-3

Now, we can rewrite the integral as:

∫(X^-2 + X^-3)dx

Now, we can integrate each term separately.

∫X^-2 dx = (1/-1)X^-1 + C = -X^-1 + C

∫X^-3 dx = (1/-2)X^-2 + C = -1/2X^-2 + C

Therefore, the final result of the integration is:

∫(X^-2 + X^-3)dx = -X^-1 - 1/2X^-2 + C

where C is the constant of integration.