# How to add integration constant

66 views (last 30 days)
Emre Tunc on 25 Sep 2016
Answered: Nathan Hall on 5 Apr 2021
I couldn't lose this function
syms a t
f(t)=-a
F(t)=int(a) (When I integrated)
=-at
but I want to add a constant with a letter which has to have:
F(t)=-at+C
How can I add a constant for indefinite integrals?

Philip M on 24 Jan 2020
Bit of a late response, but this post is still getting 50 views per month and there doesn't seem to be an answer to this question out there anywhere, so here you go.
Putting that into MATLAB format and solving using the differential equations solution function, dsolve:
syms t a F(t)
f(t) = -a;
eqn = diff(F(t))==f(t);
sol=dsolve(eqn)
sol =
C1 - a*t
Voilà! It also works for more complex equations:
syms t a F(t)
f(t)=(t^4-1/t)/sqrt(2*a*t)-(a*t)^5;
eqn=diff(F(t))==f(t);
sol=dsolve(eqn)
sol =
C1 - (a^5*t^6)/6 + 2^(1/2)/(a^(1/2)*t^(1/2)) + (2^(1/2)*t^(9/2))/(9*a^(1/2))
as well as for higher order integrals:
syms t a F(t)
f(t)=(t^4-1/t)/sqrt(2*a*t)-(a*t)^5;
eqn=diff(F(t),t,t,t)==f(t);
sol=dsolve(eqn)
sol =
C3 + C2*t + (C1*t^2)/2 + (1716*2^(1/2)*t^(3/2) + 4*2^(1/2)*t^(13/2))/(1287*a^(1/2)) - (a^5*t^8)/336
I'm perplexed as to why this workaround is even necessary and why this isn't just an option of the int feature, and why nobody has posted this solution yet. In fact, I trekked through three whole pages of Google results and this is the only instance I could find of someone even asking about it.
But oh well, there's an answer out there for it now.
Joel Silva on 18 Feb 2021
Thank you very much. This is exactly what I was looking for.

Nathan Hall on 5 Apr 2021
syms t C0 C1 C2;
a(t) = C0
v(t) = int(a(t),t) + C1
d(t) = int(v(t),t) + C2