I can't integrate cause of math range error

Question

I can't integrate this in python (1/1+t))+(-1/exp(t)) [0,np.inf]

import numpy as np
from math import exp
from scipy.integrate import quad

print(quad(lamba t: (1/1+t))+(-1/exp(t)),0,np.inf)

It must show Euler constant

Answer 1

By the way, with this integral you will never have the Euler constant.

Euler constant is defined as (sorry I can't post images):

https://i.stack.imgur.com/z6iiM.jpg

So you have to change your lambda function to the following:

import numpy as np
from math import exp
from scipy.integrate import quad
f = lambda t: 1/t * (1/(1+t) - exp(-t))

In [21]: quad(f, 0.0, np.inf)
Out[21]: (0.5772156649015537, 3.613579096292482e-10)

The result is 0.5772156649015537 which is the value of the Euler constant.

Answer 2

You wrote lamba instead of lambda, which should raise a SyntaxError.

Besides, reading your equation, the function you pass should rather be:

lambda t: 1/(1+t) - exp(-t)

Try changing your last line to:

print(quad(lambda t: (1/(1+t) - exp(-t)), 0, np.inf))