Solving integral using matlab

i need to find a percentage error between 1) and 2)

1) finding integral using "int" function (numerical result) i was able to run it easily using

fun = @(x) (exp(x)./(10*x-1));

Q2 = vpa (integral(fun, 0, 200))

BUT, when i did

2) finding integral using symbolic math tool box (exact value), I GOT X2 =NaN

syms x

X2 = vpa(int(exp(x)./(10*x-1),0,200))

MY QUESTION IS: WHY NaN

here is the picture of a question

Answer 1

[Walter Roberson]

The denominator of the function has 10*x-1 . The range of x values passes through 1/10, at which point 10*(1/10) - 1 = 1 - 1 = 0. Therefore the function passes through exp(1/10)/0 . From below, 10*x-1 is negative, so from below it approaches negative infinity as x gets closer to 1/10, and from above 10*x-1 is positive, so it approaches positive infinity from the right of x = 1/10.

So... you have a classical non-removal discontinuity, and there is no Cauchy Principal Value available either. So the integral is undefined, which MATLAB signals to you as NaN.

[Paul]

With R2026a, int returns a Cauchy PV if requested.

syms x
f(x) = exp(x)./(10*x-1)

f(x) = 

I = int(f(x),x,0,200,'PrincipalValue',true)

I = 

vpa(I)

ans = 

3.6330609856035063237447128296869e+83