A) \[\tan x+\cot x+c\]
B) \[\tan x-\cot x+c\]
C) \[\text{cosec}\,x-\cot x+c\]
D) \[\sec x-\text{cosec}\,x+c\]
Correct Answer: D
Solution :
\[\int_{{}}^{{}}{\frac{{{\sin }^{3}}x+{{\cos }^{3}}x}{{{\sin }^{2}}x{{\cos }^{2}}x}\,dx}=\int_{{}}^{{}}{\left( \frac{\sin x}{{{\cos }^{2}}x}+\frac{\cos x}{{{\sin }^{2}}x} \right)\,dx}\] \[=\frac{{{(x-5)}^{-2+1}}}{-2+1}+c=\frac{{{(x-5)}^{-1}}}{-1}+c\]\[=\sec x-\cos \text{ec}x+c\]
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