A) \[\cot x+\frac{{{\cot }^{3}}x}{3}+c\]
B) \[\tan x+\frac{{{\tan }^{3}}x}{3}+c\]
C) \[-\cot x-\frac{{{\cot }^{3}}x}{3}+c\]
D) \[-\tan x-\frac{{{\tan }^{3}}x}{3}+c\]
Correct Answer: C
Solution :
\[=-\log ({{\cos }^{-1}}x)+c.\]\[=\int{\text{cose}{{\text{c}}^{2}}x}.\,\text{cose}{{\text{c}}^{2}}xdx\] \[=\int{\text{cose}{{\text{c}}^{2}}x(1+{{\cot }^{2}}x)\,dx}\] \[=\int{\text{cose}{{\text{c}}^{2}}x\,\,dx}\,\,+\int{{{\cot }^{2}}x.\,\text{cose}{{\text{c}}^{2}}x\,dx}\] \[=-\cot x-\frac{{{\cot }^{3}}x}{3}+c\].
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