How to calculate indefinite integral?

Hello, I hope you den help me. I am doing my math homework and I want to check the answer in Matlab. However, I checked that the answer, that is given by Matlab, is wrong. Here is an example of what I wrote:

>> syms x >> int(sin(2*x-3), x) >> ans = sin(x-3/2)^2

But the correct answer is -cos(3-2x)/2 + C So maybe you can tell me what I do wrong because I am new in Matlab so it is quite hard. Thank you very much for your help!

Best regards, Don

Answer 1

[Brendan Hamm]

First off the answer is -cos(2*x-3)/2 + C. The two statements are equivalent up to a constant. Using the half angle identity:

sin(u)^2 = 1/2 - 1/2*cos(2*u)

let u = x -3/2

sin(x-3/2)^2 + C = 1/2 - 1/2*cos(2*(x-3/2)) + C

sin(x-3/2)^2 + C = -1/2*cos(2*x-3) + D

Answer 2

[Sean de Wolski]

Both answers are right, just simplified differently:

syms x
mupad_answer = int(sin(2*x-3), x)

your_answer = -cos(3-2*x)/2;

isequal(simplify(diff(your_answer)),simplify(diff(mupad_answer)))