1. ## tough integral

integrate ((10e^(-5000t))*(50(1-e^(-5000t)))) dt from 0 to 1

I got as far as :

((-1/5000)*500e^(-5000t))-500*integral((-1/e^(5000t))^2 dt

But I cant figure out the integral of (-1/e^-5000t)^2. Please, Can anyone show me how to do this ?

2. ## Re: tough integral

Originally Posted by frankinaround
integrate ((10e^(-5000t))*(50(1-e^(-5000t)))) dt from 0 to 1

I got as far as :

((-1/5000)*500e^(-5000t))-500*integral((-1/e^(5000t))^2 dt

But I cant figure out the integral of (-1/e^-5000t)^2. Please, Can anyone show me how to do this ?
$\left(-\frac{1}{e^{5000t}}\right)^2=e^{-10000t}$

CB

3. ## Re: tough integral

Originally Posted by frankinaround
integrate ((10e^(-5000t))*(50(1-e^(-5000t)))) dt from 0 to 1

I got as far as :

((-1/5000)*500e^(-5000t))-500*integral((-1/e^(5000t))^2 dt

But I cant figure out the integral of (-1/e^-5000t)^2. Please, Can anyone show me how to do this ?
You are making things difficult for yourself by not simplifying this integral as much as possible before trying to evaluate it.

$\int_0^1 (10e^{-5000t})(50(1-e^{-5000t})dt=500\int_0^1e^{-5000t}(1-e^{-5000t})\;dt$

Now you may notice that the integrand is a multiple of the derivative of $1-e^{-5000t}$, and so can be integrated immediately. Or you could make the substitution $u=5000t$ first, then make the observation...

CB