X^-3(x+1)dx integrate

Answer 1

To integrate the given expression, first distribute the x^-3 term:

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

Now, integrate each term separately with respect to x:

∫x^-2 dx = (x^-1)/(-1) = -1/x + C

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

Therefore, the final integrated expression is:

-1/x - 1/(2x^2) + C