³x + ³x/²x²x - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.3
Find the integrals of the functions in Exercises 62 to 83.

Question : 78 of 271

Marks: +1, -0

\frac{\sin^3x + \cos^3x}{\sin^2x\cos^2x}

Solution:

Let

I = \int \frac{\sin^3x + \cos^3x}{\sin^2x\cos^2x} \, dx

= \int \left( \frac{\sin^3x}{\sin^2x\cos^2x} + \frac{\cos^3x}{\sin^2x\cos^2x} \right) dx

= \int (\sec x + \tan x + \csc x \cot x) \, dx

= \sec x - \csc x + C

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