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
Fresh day, fresh solve. To solve the integral ^5 x ^4 x \, dx: Step 1: Rewrite the integrand using trigonometric identities. We know that ^2 x = 1 + ^2 x. We can split ^4 x into ^2 x · ^2 x. ^5 x ^4 x \, dx = ^5 x ^2 x ^2 x \, dx Substitute ^2 x = 1 + ^2 x for one of the ^2 x terms. ^5 x (1 + ^2 x) ^2 x \, dx Step 2: Perform a substitution. Let u = x. Then, the differential du = ^2 x \, dx. Step 3: Substitute u and du into the integral. u^5 (1 + u^2) \, du Step 4: Expand the integrand. (u^5 + u^7) \, du Step 5: Integrate term by term using the power rule x^n \, dx = x^n+1n+1 + C. u^5+15+1 + u^7+17+1 + C (u^6)/(6) + (u^8)/(8) + C Step 6: Substitute back u = x. (^6 x)/(6) + (^8 x)/(8) + C The final answer is (^6 x)/(6) + (^8 x)/(8) + C. Send me the next one 📸