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  • Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 23

Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 23

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best_answer

\sec x-\cos ec x+c

Hint:To solve this equation we separate the term then differentiate

\begin{aligned} &\text { Given: } \int \frac{\sin ^{3} x-\cos ^{3} x}{\sin ^{2} x \cdot \cos ^{2} x} d x \\ &\text { Solution: } \int \frac{\sin ^{3} x-\cos ^{3} x}{\sin ^{2} x \cdot \cos ^{2} x} d x \\ &\int \frac{\sin ^{3} x}{\sin ^{2} x \cdot \cos ^{2} x} d x-\int \frac{\cos ^{3} x}{\sin ^{2} x \cdot \cos ^{2} x} d x \\ &=\int \tan x \sec x d x-\int \cot x \cdot \cos \operatorname{ccx} d x \end{aligned}

\sec x-\cos ec x+c

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