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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 53

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 53

Answers (1)

Answer: \frac{1}{4}\tan^{-1}\left ( \frac{x}{4} \right )+c

Hints: You must know about rules of integration

Given: 

\int \frac{1}{x^{2}+16}dx

Solution:

\begin{aligned} &\int \frac{1}{x^{2}+16} d x \\ &=\int \frac{1}{x^{2}+(4)^{2}} d x \\ &\quad \int \frac{1}{x^{2}+4^{2}} d x=\frac{1}{4} \tan ^{-1}\left(\frac{x}{4}\right)+c \quad\quad\quad\quad\quad \int \frac{1}{x^{2}+a^{2}} d x=\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+c \end{aligned}

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