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Evaluate the following integrals :\(\int\frac{-sin\,x+2cos\,x}{2sinx+cosx}\)dx |
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Answer» Assume, 2sinx + cosx = t d(2sinx + cosx) = dt (2cosx - sinx)dx = dt Put t and dt in given equation we get ⇒ ∫\(\frac{dt}{t}\) = In|t| + c But, t = 2sinx + cosx = ln|2sinx + cosx| + c. |
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