Short Answer

Solve the integral
$\int \frac{1}{x^{2} \sqrt{x^{2} - 9}} d x$

$\frac{\sqrt{x - 3}}{9 x} \sqrt{x + 3} + C$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given

$\int \frac{1}{x^{2} \sqrt{x^{2} - 9}} d x$

Step 2. Using identity

$To solve the integral, let x = 3 \cosh (u) . Now, derivation of the above equation is solved below . x = 3 \cos h (u) d x = 3 \sin h ((u) d u) Now, use the identity c o s h^{2} (u) - 1 = s i n h^{2} (u) S o, \frac{1}{x^{2} \sqrt{x^{2} - 9}} = \frac{1}{(9 \sqrt[]{(9 \cos h^{2} (u) - 9)} c o s h^{2} (u))} = \frac{1}{27 \sqrt{\cos h^{2} (u)} - 1 c o s h^{2} (u)} = \frac{1}{27 \sqrt{s i n h^{2} (u}) c o s h^{2} (u)} = \frac{1}{27 s i n h (u) c o s h^{2} (u)}$

Step 3. Calculation

$\frac{1}{x^{2} \sqrt{x^{2} - 9}} = \int \frac{1}{9 c o s h^{2} (u)} d u = \frac{1}{t a n h (u)} + C = \frac{1}{9 t a n h (c o s h^{-} 1 (\frac{x}{2}))} + C = \frac{\sqrt{\frac{x}{3} + 1}}{3 x} \sqrt{\frac{x}{3} - 1} + C = \frac{\sqrt{x - 3}}{9 x} \sqrt{x + 3} + C Therefore, the value is boxed \frac{\sqrt{x - 3}}{9 x} \sqrt{x + 3} + C$

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

Solve the integral
$\int \frac{1}{x^{2} \sqrt{x^{2} - 9}} d x$

Step by Step Solution

Step 1. Given

Step 2. Using identity

Step 3. Calculation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

Solve the integral∫1x2x2-9dx

Step by Step Solution

Step 1. Given

Step 2. Using identity

Step 3. Calculation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Calculus

Pure Maths

Solve the integral
$\int \frac{1}{x^{2} \sqrt{x^{2} - 9}} d x$