Question
Download Solution PDF\(\rm \int\frac{e^{tan^{-1}x}}{1+x^2}dx=?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation -
We have \(I =\rm \int\frac{e^{tan^{-1}x}}{1+x^2}dx\)
Let \(tan^{-1}x= t \implies \frac{1}{1+x^2} dx =dt\)
Now we get -
\(I= \int e^t dt= e^t +C\)
\(I= e^{tan^{-1}x} +C\)
Hence the option (1) is correct.
Last updated on May 26, 2025
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