I'm getting a negative part in Time complexity function. Is the solution of the Time complexity of this Recurrence relation correct?

Question

I tried to find the Time complexity of this Recurrence relation [T(n) = 7T(n/2) + n^2] by using Akra Bazzi method .But I am not sure if it's correct or not. Can someone please review the solution and let me know if I made any mistake anywhere?

This is my solution of the Recurrence relation [T(n) = 7T(n/2) + n^2]

My Time complexity answer is matching with the WolframAlpha calculator. But I am not sure if I did the internal workings correctly since I'm getting a negative part in the Time complexity function.

Answer 1

I searched on your doubt , inside teh integrate value ubr getting ignore it less dominating term. 0[2 (x^log2^7)] Ignore constan, value of log2^7 = 2.8 Therefore,

0(n^2.8) approximately 0(n^3)