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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 40

Answers (1)

Answer: 2\tan \sqrt{x}+c

Hint: You must know about the integral rule of trigonometric functions

Given:  \int \frac{\sec^{2}\sqrt{x}}{\sqrt{x}}dx

Solution:

\int \frac{\sec^{2}\sqrt{x}}{\sqrt{x}}dx

Let,

 \begin{aligned} &t=\tan \sqrt{x} d x \\ &d t=\frac{\sec ^{2} \sqrt{x}}{2 \sqrt{x}} d x \\ &2 d t=\frac{\sec ^{2} \sqrt{x}}{\sqrt{x}} d x \\ &=\int 2 d t \\ &=2 t+c \\ &=2 \tan \sqrt{x}+c \end{aligned}                                                                  

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