Evaluate `int_(-4)^(-5)e^((x+5^(2))) dx+3int_(1//3)^(2//3)e^(9(x-(2)/(3))^(2)dx`

Explanation

Here we change the limits to `0` and `1`, using
`int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx`
Now,
`l_(1)=int_(-4)^(-5)e^((x+5)^(2))dx`
`=(-5+4)int_(0)^(1)e^(}(-5+4)x-4+5}^(2))dx`
`=-int_(0)^(1)e^((1-x)^(2))dx`
`=-int_(0)^(1)e^((x-1)^(2))dx`.............`(i)`
Again let,
`l_(2)=int_((1)/(3))^((2)/(3))e^(9(x-(3)/(3))^(2))dx`
`=((2)/(3)-(1)/(3))int_(0)^(1)e^(9{((2)/(3)-(1)/(3))x+(1)/(3)-(2)/(3)}^(2))dx`
`=(1)/(3)int_(0)^(1)e^(9((x)/(3)-(1)/(3))^(2))dx`
`=(1)/(3)int_(0)^(1)e^((x-1)^(2))dx`..........`(ii)`
`(i)` and `(ii)` together yield
`l_(1)+3l_(2)=0`