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Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise18.5 Question 6 Maths Textbook Solution.

Answers (1)

Answer: \frac{2}{49}(7 x+17) \sqrt{7 x+9}+C

Hint: Try to take out common factors

Given: \int \frac{(3 x+5)}{\sqrt{7 x+9}} d x \\

Solution: On multiplying and dividing by 3 in the equation, we get

\begin{aligned} &=\int \frac{(3 x+5)}{\sqrt{7 x+9}} d x \\ &=3 \int \frac{x+\frac{5}{3}}{\sqrt{7 x+9}} d x \end{aligned}


\begin{aligned} &I=\frac{3}{7} \int \frac{7 x+\frac{35}{3}}{\sqrt{7 x+9}} d x \\ &I=\frac{3}{7} \int \frac{7 x+9-9+\frac{35}{3}}{\sqrt{7 x+9}} d x \\ &I=\frac{3}{7} \int \frac{7 x+9+\frac{8}{3}}{\sqrt{7 x+9}} d x \end{aligned}


\begin{aligned} &I=\frac{3}{7} \int \frac{7 x+9}{\sqrt{7 x+9}} d x+\int \frac{8}{7} \cdot \frac{1}{\sqrt{7 x+9}} d x \\ &I=\frac{3}{7} \int \sqrt{7 x+9} d x+\int \frac{8}{7} \cdot \frac{1}{\sqrt{7 x+9}} d x \end{aligned}


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