Mathematics

Mathematics

Problem

∫sin⁡xcos⁡xacos⁡2x+bsin⁡2x dx=\int \frac{\sin x\cos x}{a \cos^2 x + b \sin^2 x}\,dx = (a) 12(b−a)log⁡(acos⁡2x+bsin⁡2x)+c\frac{1}{2(b-a)}\log(a \cos^2 x + b \sin^2 x) + c (b) 1b−alog⁡(acos⁡2x+bsin⁡2x)+c\frac{1}{b-a}\log(a \cos^2 x + b \sin^2 x) + c (c) 12log⁡(acos⁡2x+bsin⁡2x)+c\frac{1}{2}\log(a \cos^2 x + b \sin^2 x) + c (d) None of these (a) 12(b−a)log⁡(acos⁡2x+bsin⁡2x)+c\frac{1}{2(b-a)}\log(a \cos^2 x + b \sin^2 x) + c (b) 1b−alog⁡(acos⁡2x+bsin⁡2x)+c\frac{1}{b-a}\log(a \cos^2 x + b \sin^2 x) + c (c) 12log⁡(acos⁡2x+bsin⁡2x)+c\frac{1}{2}\log(a \cos^2 x + b \sin^2 x) + c (d) None of these

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