int frac{sin^3(x) + cos^3(x)}{sin^2(x) cdot c | vedclass

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Question

(A) આપેલ સંકલન: $I = \int \frac{\sin^3(x) + \cos^3(x)}{\sin^2(x) \cos^2(x)} \, dx$ અંશના દરેક પદને છેદ વડે ભાગતા: $I = \int \left( \frac{\sin^3(x)}{\s

Vedclass · Accepted Answer

$\sec(x) - \operatorname{cosec}(x) + C$

Vedclass · Answer

(A) આપેલ સંકલન: $I = \int \frac{\sin^3(x) + \cos^3(x)}{\sin^2(x) \cos^2(x)} \, dx$ અંશના દરેક પદને છેદ વડે ભાગતા: $I = \int \left( \frac{\sin^3(x)}{\sin^2(x) \cos^2(x)} + \frac{\cos^3(x)}{\sin^2(x) \cos^2(x)} ight) \, dx$ $I = \int \left( \frac{\sin(x)}{\cos^2(x)} + \frac{\cos(x)}{\sin^2(x)} ight) \, dx$ ત્રિકોણમિતીય નિત્યસમનો ઉપયોગ કરતા: $I = \int (	an(x) \sec(x) + \cot(x) \operatorname{cosec}(x)) \, dx$ દરેક પદનું સંકલન કરતા: $\int \sec(x) 	an(x) \, dx = \sec(x)$ $\int \operatorname{cosec}(x) \cot(x) \, dx = -\operatorname{cosec}(x)$ તેથી,$I = \sec(x) - \operatorname{cosec}(x) + C$. આમ,વિકલ્પ $A$ સાચો છે.

$\int \frac{\sin^3(x) + \cos^3(x)}{\sin^2(x) \cdot \cos^2(x)} \, dx = $

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