Integrate the following functions w.r.t. x : e2x+1e2x-1 - Mathematics and Statistics

प्रश्न

Integrate the following functions w.r.t. x : $\frac{e^{2 x} + 1}{e^{2 x} - 1}$

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उत्तर

Let I = $\int \frac{e^{2 x} + 1}{e^{2 x} - 1} . d x$

= $\int \frac{(\frac{e^{2 x} + 1}{e^{x}})}{(\frac{e^{2 x} - 1}{e^{x}})} . d x$

= $\int (\frac{e^{x} + e^{- x}}{e^{x} - e^{- x}}) . d x$

= $\int \frac{\frac{d}{d x} (e^{x} - e^{- x})}{e^{x} - e^{- x}} . d x$

= log|e^x – e^–x| + c. ... $[∵ \int \frac{f' (x)}{f (x)} . d x = \log | f (x) | + c]$

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Methods of Integration: Integration by Substitution

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 1.08 Q 1.07 Q 1.09

पाठ 3: Indefinite Integration - Exercise 3.2 (A) [पृष्ठ ११०]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board

पाठ 3 Indefinite Integration
Exercise 3.2 (A) | Q 1.08 | पृष्ठ ११०

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Integrate the following functions w.r.t. x : e2x+1e2x-1 - Mathematics and Statistics

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Integrate the following functions w.r.t. x : e2x+1e2x-1 - Mathematics and Statistics

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