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
🤍🦋Mashiyamahle🤍🦋, let's knock this out. The problem asks to evaluate the indefinite integral: ( x^2 - (5)/(x) + 3 ^2 x + 5 3x - (6)/(x) ) dx Step 1: Combine like terms in the integrand. The terms -(5)/(x) and -(6)/(x) can be combined. -(5)/(x) - (6)/(x) = -(11)/(x) So the integral becomes: ( x^2 - (11)/(x) + 3 ^2 x + 5 3x ) dx Step 2: Integrate each term separately using the standard integration rules. Recall the rules: • x^n dx = x^n+1n+1 + C (for n ≠ -1) • (1)/(x) dx = |x| + C • ^2 x dx = x + C • (ax) dx = -(1)/(a) (ax) + C Step 3: Integrate x^2. x^2 dx = x^2+12+1 = (x^3)/(3) Step 4: Integrate -(11)/(x). -(11)/(x) dx = -11 (1)/(x) dx = -11 |x| Step 5: Integrate 3 ^2 x. 3 ^2 x dx = 3 ^2 x dx = 3 x Step 6: Integrate 5 3x. 5 3x dx = 5 ( -(1)/(3) 3x ) = -(5)/(3) 3x Step 7: Combine all the integrated terms and add the constant of integration, C. (x^3)/(3) - 11 |x| + 3 x - (5)/(3) 3x + C The final answer is: (x^3)/(3) - 11 |x| + 3 x - (5)/(3) 3x + C Send me the next one 📸