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Question

Question: \(\frac{1}{2}\cos^{- 1}(\log x) + c\)...

12cos⁡−1(log⁡x)+c\frac{1}{2}\cos^{- 1}(\log x) + c

A

∫f′(x)[f(x)]2 6mudx=\int_{}^{}\frac{f'(x)}{\lbrack f(x)\rbrack^{2}}\mspace{6mu} dx =

B

−[f(x)]−1+c- \lbrack f(x)\rbrack^{- 1} + c

C

log⁡[f(x)]+c\log\lbrack f(x)\rbrack + c

D

ef(x)+ce^{f(x)} + c

Answer

ef(x)+ce^{f(x)} + c

Explanation

Solution

∫sin⁡xcos⁡xacos⁡2x+bsin⁡2xdx=\int_{}^{}{\frac{\sin x\cos x}{a\cos^{2}x + b\sin^{2}x}dx =}

12(b−a)log⁡(acos⁡2x+bsin⁡2x)+c\frac{1}{2(b - a)}\log(a\cos^{2}x + b\sin^{2}x) + c.