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Explain Solution R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.19 Question 15 maths Textbook Solution.

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Answer:\log \frac{|3 x+4|}{3}+c

Hint: Solve Integration

Given: \int \frac{x+7}{3 x^{2}+25 x+28} d x


            \begin{aligned} &\int \frac{x+7}{3 x^{2}+25 x+28} d x \\ &=\int \frac{x+7}{3 x^{2}+21 x+4 x+28} d x \\ &=\int \frac{x+7}{3 x(x+7)+4(x+7)} d x \\ &=\int \frac{x+7}{(3 x+4)(x+7)} d x \\ &=\int \frac{d x}{3 x+4} \end{aligned}

            Let,\begin{aligned} &3 x+4=t \\ &3 d x=d t \end{aligned}

                  d x=\frac{d t}{3}

  \begin{aligned} &=\int \frac{d t}{3 t}+c \\ &=\frac{1}{3} \log |3 x+4|+c \end{aligned}

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