Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals2 Marks
Question
Evaluate $\int \frac{\sin ^3 x+\cos ^3 x}{\sin ^2 x \cos ^2 x} d x$.
✓
Answer
$\int \frac{\sin ^3 x+\cos ^3 x}{\sin ^2 x \cos ^2 x} d x$ $ \begin{array}{l} =\int\left(\frac{\sin ^3 x}{\sin ^2 x \cos ^2 x}+\frac{\cos ^3 x}{\sin ^2 x \cos ^2 x}\right) d x \\ =\int\left(\frac{\sin x}{\cos ^2 x}+\frac{\cos x}{\sin ^2 x}\right) d x \\ =\int(\tan x \sec x+\cot x \operatorname{cosec} x) d x \\ =\int \tan x \sec x d x+\int \cot x \operatorname{cosec} x d x \\ =\sec x-\operatorname{cosec} x+C \end{array} $
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