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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS2 Marks
Question
Find the integrals of the functions in Exercises:
$\frac{\sin^3\text{x}+\cos^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}$
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Answer

$\frac{\sin^3\text{x}+\cos^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}$
$=\frac{\sin^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}+\frac{\cos^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}$
$=\frac{\sin\text{x}}{\cos^2\text{x}}+\frac{\cos\text{x}}{\sin^2\text{x}}$
$=\tan\text{x}\sec\text{x}+\cot\text{x}\text{ cosec x}$
$\therefore\ \ \ \int\frac{\sin^3\text{x}+\cos^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{ dx}=\int\big(\tan\text{x}\sec\text{x}+\cot\text{x}\text{ cosec x}\big)\text{dx}$
$=\sec\text{x}-\text{cosec x}+\text{C}$

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