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Question

Question: \({logsin}(\log x) + c\)...

logsin(logx)+c{logsin}(\log x) + c

A

logsec(logx)+c{logsec}(\log x) + c

B

logcosec(logx)+c\log c\text{osec}(\log x) + c

C

cos3x6muelog(sinx)6mudx\int_{}^{}{\cos^{3}x\mspace{6mu} e^{\log(\sin x)}}\mspace{6mu} dx

D

None of these

Answer

logcosec(logx)+c\log c\text{osec}(\log x) + c

Explanation

Solution

Put 4x2+12x+6logx1x+c4x^{2} + 12x + 6\log x - \frac{1}{x} + c then

4x2+12x6logx2x+c4x^{2} + 12x - 6\log x - \frac{2}{x} + c

2x2+8x+3logx2x+c2x^{2} + 8x + 3\log x - \frac{2}{x} + c