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  • Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.28 Question 8 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.28 Question 8 Maths Textbook Solution.

Answers (1)

best_answer

Answer:-

2 x \sqrt{x^{2}+\frac{25}{16}}+\frac{25}{8} \log \left[x+\sqrt{x^{2}+\frac{25}{16}}\right]+c

Hint:-

Taking common 4 and then use the formula.

Given:-

\int \sqrt{16 x^{2}+25} d x

Solution:-

\begin{aligned} &=4 \int \sqrt{x^{2}+\frac{25}{16}} d x \\\\ &=4 \int \sqrt{(x)^{2}+\left(\frac{5}{4}\right)^{2}} d x \\\\ &=4\left[\frac{1}{2} x \sqrt{(x)^{2}+\left(\frac{5}{4}\right)^{2}}+\frac{1}{2} \times \frac{25}{16} \log \left[x+\sqrt{x^{2}+\frac{25}{16}}\right]+c\right] \end{aligned}

 

Using the formula

\begin{aligned} &\int \sqrt{x^{2}+a^{2}} d x=\frac{x}{2} \sqrt{x^{2}+a^{2}}+\frac{a^{2}}{2} \log \left|x+\sqrt{x^{2}+a^{2}}\right|+c \\\\ &=2 x \sqrt{x^{2}+\frac{25}{16}}+\frac{25}{8} \log \left[x+\sqrt{x^{2}+\frac{25}{16}}\right]+c \end{aligned}

 

 

 

 

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