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प्रश्न
`int (dx)/(e^x + e^(-x))` is equal to ______.
विकल्प
`tan^-1 (e^x) + c`
`tan^-1 (e^-x) + c`
`log (e^x - e^-x) + c`
`log (e^x + e^-x) + c`
MCQ
रिक्त स्थान भरें
उत्तर
`int (dx)/(e^x + e^(-x))` is equal to `underlinebb(tan^-1 (e^x) + c)`.
Explanation:
Let I = `int (dx)/(e^x + e^-x)`
= `int (dx)/(e^x + 1/e^x)`
= `int (e^x dx)/(e^(2x) + 1)`
Put `e^x = t, e^x dx = dt`
I = `int 1/(t^2 + 1) dt = tan^-1 t + c = tan^-1 (e^x) + c`
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