Question
Integrate x^-3(X+1)
Answers
GPT 3.5
To integrate x^-3(X+1), we first need to expand the expression:
x^-3(X+1) = x^-3 * X + x^-3 * 1
= x^-2 + x^-3
Now we can integrate each term separately:
∫ x^-2 dx = x^(-2+1) / (-2+1) + C
= x^-1 / -1 + C
= -1/x + C
∫ x^-3 dx = x^(-3+1) / (-3+1) + C
= x^-2 / -2 + C
= -1/(2x^2) + C
Therefore, the integral of x^-3(X+1) is:
∫ x^-3(X+1) dx = -1/x + (-1/(2x^2)) + C
= -1/x - 1/(2x^2) + C
x^-3(X+1) = x^-3 * X + x^-3 * 1
= x^-2 + x^-3
Now we can integrate each term separately:
∫ x^-2 dx = x^(-2+1) / (-2+1) + C
= x^-1 / -1 + C
= -1/x + C
∫ x^-3 dx = x^(-3+1) / (-3+1) + C
= x^-2 / -2 + C
= -1/(2x^2) + C
Therefore, the integral of x^-3(X+1) is:
∫ x^-3(X+1) dx = -1/x + (-1/(2x^2)) + C
= -1/x - 1/(2x^2) + C