# Confusion in finding the definite integral

So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different. Can someone please point out what I'm missing? The answer from wolframAlpha is correct according to Casio fx-991-es

Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, {t, -0.8, 0}]


• Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images. – user6014 Sep 9 '18 at 1:43
• oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, {t, -0.8, 0}] – Ramith Hettiarachchi Sep 9 '18 at 1:45

Precision issues. Use one of the following instead.

Symbolic integration:

Integrate[(1/(1 + t)) ((t + 4/5)/(t + 1))^20, {t, -4/5, 0}]
(*-(318650448087859023644/198221683502197265625) + Log[5]*)

N@%
(*0.00189205*)


Numeric integration with a higher working precision:

NIntegrate[(1/(1 + t)) ((t + .820)/(t + 1))^20, {t, -.820, 0}]
(*0.00189205*)

• Usually when do these issues occur? should i use NIntegrate instead? – Ramith Hettiarachchi Sep 9 '18 at 1:52
• These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require. – user6014 Sep 9 '18 at 1:54
• There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results – user6014 Sep 9 '18 at 1:55
• Appreciate your help 🙌Thanks! – Ramith Hettiarachchi Sep 9 '18 at 1:57
• @RamithHettiarachchi -- (1) Note further that if you do just add an N in front of your Integrate[..], you get the same answer as the NIntegrate[..] in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such as Integrate often have trouble with "inexact" floating-point input. (3) Interesting aside: Integrate[(1/(1 + t)) ((t + .820)/(t + 1))^20, {t, -.820, 0}] caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems. – Michael E2 Sep 9 '18 at 19:02