Integration showing wrong answer

Answer 1

[Star Strider]

It is the correct result, although it may not be the one you were anticipaiting.

Try this:

syms x 
f(x) = sin(x)+2*cos(x)
intf = int(f)
simplifiedResult = simplify(intf, 'Steps', 100)

producing:

f(x) =
2*cos(x) + sin(x)
 
intf(x) =
-2*cos(x/2)*(cos(x/2) - 2*sin(x/2))
 
simplifiedResult(x) =
2*sin(x) - cos(x) - 1