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Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.3 Question 2 Maths Textbook Solution.

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Answer: \frac{-1}{14}(7 x-5)^{-2}+\frac{2}{5} \sqrt{5 x-4}+c

Hint:To solve this we take denominator as numerator

Given: \int \frac{1}{(7 x-5)^{3}}+\frac{1}{\sqrt{5 x-4}} d x

Solution: \int(7 x-5)^{-3} d x+\int(5 x+4)^{\frac{1}{2}}

\begin{aligned} &\int(a x+b)^{n} d x=\frac{1}{a(n+1)}(a x+b)^{n+1}+c ; n \neq-1 \\ &=\frac{1}{7} \frac{(7 x-5)^{-2}}{-2}+\frac{1}{5} \frac{(5 x+4)^{\frac{1}{2}}}{\frac{1}{2}}+c \end{aligned}

\begin{aligned} &=\frac{-1}{14}(7 x-5)^{-2}+\frac{2}{5} \sqrt{5 x-4}+c \\ &=\frac{-1}{14}(7 x-5)^{-2}+\frac{2}{5} \sqrt{5 x-4}+c \end{aligned}

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