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  • Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 24

Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 24

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\frac{-5}{2} \operatorname{cosec} x+3 \sec x+c

Hint: To solve this equation we separate the terms

\begin{aligned} &\text { Given: } \int \frac{5 \cos ^{3} x+6 \sin ^{3} x}{2 \sin ^{2} x \cdot \cos ^{2} x} d x \\ &\text { Solution: } \int \frac{5 \cos ^{3} x+6 \sin ^{3} x}{2 \sin ^{2} x \cdot \cos ^{2} x} d x \\ &\int \frac{5 \cos ^{3} x}{2 \sin ^{2} x \cdot \cos ^{2} x} d x-\int \frac{6 \sin ^{3} x}{2 \sin ^{2} x \cdot \cos ^{2} x} d x \\ &=\frac{5}{2} \int \frac{\cos x}{\sin ^{2} x} d x-3 \int \frac{\sin x}{\cos ^{2} x} d x \\ &=\frac{5}{2}\int(\cot x \cos e c x)dx+3\int \tan x \sec xdx \\ &=\frac{-5}{2} \cos e c x+3 \sec x+c \end{aligned}

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