Integration of Exponential Function with Limits from 0 to t

[matt222]

Homework Statement

integrate the function F(t)=1-exp(-∫1/t+2 dt) limit of integration from 0 to t

Homework Equations

The Attempt at a Solution

F(t)=1-exp(-ln(t+2)+ln2)
=1-exp(ln(2-t))*exp(ln2)
=1+2t-4
=2t-3

what do you think about my solutions?

 

[LCKurtz]

Homework Statement

integrate the function F(t)=1-exp(-∫1/t+2 dt) limit of integration from 0 to t

Homework Equations

The Attempt at a Solution

F(t)=1-exp(-ln(t+2)+ln2)
=1-exp(ln(2-t))*exp(ln2)
=1+2t-4
=2t-3

what do you think about my solutions?

I think it is full of mistakes. For one thing, it isn't clear whether your original exponential is$$e^{-\int {\frac 1 t + 2}\, dt}\hbox{ or } e^{-\int \frac{1}{t+2}\,dt}$$ In your first step you have treated it both ways and you are careless with your - signs and simplification. Try again.