int e^{sin x} frac{(x cos^3 x - sin x)}{cos^2 | vedclass

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Question

(A) माना $I = \int e^{\sin x} \left( \frac{x \cos^3 x - \sin x}{\cos^2 x} ight) dx$ $= \int e^{\sin x} (x \cos x - 	an x \sec x) dx$ यहाँ,यदि हम $f

Vedclass · Accepted Answer

$e^{\sin x}(x - \sec x) + C$

Vedclass · Answer

(A) माना $I = \int e^{\sin x} \left( \frac{x \cos^3 x - \sin x}{\cos^2 x} ight) dx$ $= \int e^{\sin x} (x \cos x - 	an x \sec x) dx$ यहाँ,यदि हम $f(x) = e^{\sin x}(x - \sec x)$ लें,तो इसका अवकलन करने पर: $\frac{d}{dx} [e^{\sin x} (x - \sec x)] = e^{\sin x} \cos x (x - \sec x) + e^{\sin x} (1 - \sec x 	an x)$ $= x e^{\sin x} \cos x - e^{\sin x} + e^{\sin x} - e^{\sin x} \sec x 	an x$ $= e^{\sin x} (x \cos x - \sec x 	an x)$ अतः,समाकलन का उत्तर $e^{\sin x}(x - \sec x) + C$ है।

$\int e^{\sin x} \frac{(x \cos^3 x - \sin x)}{\cos^2 x} dx =$

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