In the indefinite integral, what’s the integration of (e^x)/x ?
In the indefinite integral, what’s the integration of (e^x)/x ?
Ravi Chandran , 6 Years ago
Grade 12th pass
Magical Mathematics[Interesting Approach]> In the indefinite integral, what’s the in...
1 Answers
Arun
Last Activity: 6 Years ago
(e^x)/x has no elementary derivative -- you can try integration by parts but you won't get anywhere.
so mathematicians have made up a special function called the exponential integral, Ei(x), which is defined as:
Ei(x) = integral, from -infinity to x, of (e^t / t) dt
so mathematicians have made up a special function called the exponential integral, Ei(x), which is defined as:
Ei(x) = integral, from -infinity to x, of (e^t / t) dt
You cannot solve this explicitly (analytically).
However, you can do it in terms of power series!
Recall that
e^x = ∑ xⁿ/n!,so
e^x / x = 1/x + ∑ xⁿ / (n+1)!.
Therefore,
∫e^x / x dx = ln|x| + ∑ xⁿ / (n·n!) + C.
However, you can do it in terms of power series!
Recall that
e^x = ∑ xⁿ/n!,so
e^x / x = 1/x + ∑ xⁿ / (n+1)!.
Therefore,
∫e^x / x dx = ln|x| + ∑ xⁿ / (n·n!) + C.
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