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Question

Question: \[\log(1 + \cot x) + c\]...

log⁡(1+cot⁡x)+c\log(1 + \cot x) + c

A

−log⁡(1+cot⁡x)+c- \log(1 + \cot x) + c

B

12(1+cot⁡x)2+c\frac{1}{2(1 + \cot x)^{2}} + c

C

∫1xsin⁡x 6mudx=\int_{}^{}\frac{1}{\sqrt{x}}\sin\sqrt{x}\mspace{6mu} dx =

D

−12cos⁡x+c- \frac{1}{2}\cos\sqrt{x} + c

Answer

∫1xsin⁡x 6mudx=\int_{}^{}\frac{1}{\sqrt{x}}\sin\sqrt{x}\mspace{6mu} dx =

Explanation

Solution

logcotx+c{logcot}x + c

Put ∫11+sin⁡xdx=\int_{}^{}{\frac{1}{\sqrt{1 + \sin x}}dx} = then it reduces to

22logtan(π8+x4)+c2\sqrt{2}{logtan}\left( \frac{\pi}{8} + \frac{x}{4} \right) + c.