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प्रश्न
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
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उत्तर
Let I = `int (e^(2x) + 1)/(e^(2x) - 1).dx`
= `int (((e^(2x) + 1)/(e^x)))/(((e^(2x) - 1)/(e^x))).dx`
= `int((e^x + e^(-x))/(e^x - e^-x)).dx`
= `int (d/dx(e^x - e^-x))/(e^x - e^-x).dx`
= log|ex – e–x| + c. ...`[∵ int (f'(x))/f(x).dx= log|f(x)| + c]`
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