Problem with indefinite integral

why does the indefinite integral shows incorrect result??

how to get the constant term lost back??

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/symbolic/int.html#btydjvs-2

TIPS

• Results returned by int do not include integration constants.

If you need a constant of integration, then add one yourself.

"why does the indefinite integral shows incorrect result??"

What leads you to say that the results are wrong?

>> int(2*sin(t)+3*cos(t))

ans =

6*cos(t/2)*sin(t/2) - 4*cos(t/2)^2

>> diff(ans,t)

ans =

3*cos(t/2)^2 - 3*sin(t/2)^2 + 4*cos(t/2)*sin(t/2)

>> simplify(ans)

ans =

3*cos(t) + 2*sin(t)

Looks consistent to me.