Integration Help in exponential

Hello Everyone

I would like to know, How do I integrate the follwoing equation. Limits are from 0 to t

Please any help would be appreciable.

Thank You

Answer 1

[John D'Errico]

Did you try it? Why not make an effort? Surely you can do something.

syms t T
K(t) = exp(-t^1.3/27.290)*exp(-t/12.724)*t^0.3

K(t) = 

int(K,[0,T])

ans = 

So int is unable to find a solution. But that just means there is no symbolic solution, at least nothing int could find. I'm not totally surprised at that.

However, that does not mean nothing can be done. You can still find a numerical solution.

k = @(s) exp(-s.^1.3/27.290).*exp(-s/12.724).*s.^0.3;
kint = @(S) integral(k,0,S);

And now for any reasonable value of the upper end point limit for the integral, integral will yield a result.

kint(0.5)

ans = 0.3033

Is there anything you can write down on paper? Nope. But then there are infinitely many simple problms you can write down with no analytical solution.