This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Rewrite the integrand using negative exponents. The term (1)/(x^2) can be written as x^-2. ( (1)/(x^2) - 2x ) dx = (x^-2 - 2x^1) dx Step 2: Apply the power rule for integration, which states x^n dx = x^n+1n+1 + C for n ≠ -1. Integrate each term of the expression: For the first term, x^-2: x^-2 dx = x^-2+1-2+1 = x^-1-1 = -(1)/(x) For the second term, -2x^1: -2x^1 dx = -2 x^1+11+1 = -2 (x^2)/(2) = -x^2 Step 3: Combine the results of the integration and add the constant of integration, C. ( (1)/(x^2) - 2x ) dx = -(1)/(x) - x^2 + C The evaluated integral is -(1)/(x) - x^2 + C. What's next? Send 'em!