int e^{x operatorname{cosec} x} cdot operator | vedclass

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Question

(B) ધારો કે $I = \int e^{x \operatorname{cosec} x} \cdot \operatorname{cosec} x \cdot (1 - x \cot x) \, dx$. $t = x \operatorname{cosec} x$ આદેશ લો. $

Vedclass · Accepted Answer

$e^{x \operatorname{cosec} x} + c$

Vedclass · Answer

(B) ધારો કે $I = \int e^{x \operatorname{cosec} x} \cdot \operatorname{cosec} x \cdot (1 - x \cot x) \, dx$. $t = x \operatorname{cosec} x$ આદેશ લો. $x$ ની સાપેક્ષમાં વિકલન કરતા: $\frac{dt}{dx} = x \cdot \frac{d}{dx}(\operatorname{cosec} x) + \operatorname{cosec} x \cdot \frac{d}{dx}(x)$ $\frac{dt}{dx} = x(-\operatorname{cosec} x \cot x) + \operatorname{cosec} x(1)$ $\frac{dt}{dx} = \operatorname{cosec} x(1 - x \cot x)$ તેથી,$dt = \operatorname{cosec} x(1 - x \cot x) \, dx$. આ કિંમતો સંકલનમાં મૂકતા: $I = \int e^t \, dt = e^t + c$ $t = x \operatorname{cosec} x$ પાછું મૂકતા: $I = e^{x \operatorname{cosec} x} + c$. આમ,વિકલ્પ $B$ સાચો છે.

$\int e^{x \operatorname{cosec} x} \cdot \operatorname{cosec} x \cdot(1-x \cot x) \, dx =$

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