Matlab does not integral the long function

I'm running a project and got this function in matlab :

It1= (176567213623879289833666003849645*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/316912650057057350374175801344 + (3969*exp(-207/(1000*((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 4675603322059651/18014398509481984))))/4 + (1552493519019511649*(1 - ((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 4675603322059651/18014398509481984)^2)^(1/2))/2251799813685248 + (6035185237487246127*exp(-207/(1000*((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 4675603322059651/18014398509481984)))*((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 890695189918650103/2251799813685248000))/45035996273704960 + 2835156233222016111370674437094247/10141204801825835211973625643008

It looks long but only has one variable t, now I want to integral it from 5 to 19, I typed code like this but matlab dose not evaluate it. How do I get a value for this integration?

It2= int(It1,t,5,19)

Thanks!

Answer 1

[Ameer Hamza]

int() is used for symbolic integration. If MATLAB cannot find a closed-form expression for output, then it will just return the integral expression again. You can find a numerical solution using vpa()

It2 = int(It1,t,5,19);
It2 = vpa(It2);

Another solution is to convert the expression to floating-point format and then use integral() will be faster

It1 = (176567213623879289833666003849645*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/316912650057057350374175801344 + (3969*exp(-207/(1000*((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 4675603322059651/18014398509481984))))/4 + (1552493519019511649*(1 - ((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 4675603322059651/18014398509481984)^2)^(1/2))/2251799813685248 + (6035185237487246127*exp(-207/(1000*((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 4675603322059651/18014398509481984)))*((391473114645473*cos((pi*(15*t - 6392242573992627495/36028797018963968))/180))/562949953421312 + 890695189918650103/2251799813685248000))/45035996273704960 + 2835156233222016111370674437094247/10141204801825835211973625643008;
It1 = matlabFunction(It1)

It1 = integral(It1, 5, 19)

[Xinyu Liu]

Thank you!

[Ameer Hamza]

I am glad to be of help!!!