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$$\int{e^t\over 1+t^2}$$

I don't understand the result of this integral which is supposed to be

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Bobson Dugnutt
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Gil Valeriano
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  • Have you looked up the definition of $Ei(x) $?? It's a special function defined as $-\int_{-x}^{\infty} \frac{e^{-t}dt}{t}$. Your function can be deformed into a couple intergrals... To see how it works I recommend starting from the answer, and then use the definition I give above to simplify the two intergrals, then combine them to get your original integral. You can then just read that proof backward to get your answer!! – Brevan Ellefsen Feb 28 '16 at 18:15

1 Answers1

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Split your answer into two parts, each containing one of the Exponential Integral functions. Then rewrite the functions as integrals, simplify, and combine the integrals again. Here is how to initially set up one of the functions. $$-\frac{ie^i}{2}\text{Ei}(t-i) $$ $$\int_{i-t}^{\infty} \frac{ie^i}{2te^t}$$ This looks messy, but just make sure to your integral limits are the same for both integrals and cancelations should occur when the integrals are combined (I'm on mobile, but if you need more help and no one else provides it I can help more later)

Brevan Ellefsen
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