Advertisement Remove all ads

# ∫ 2 X Sec 3 ( X 2 + 3 ) Tan ( X 2 + 3 ) D X - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum
$\int2x \sec^3 \left( x^2 + 3 \right) \tan \left( x^2 + 3 \right) dx$
Advertisement Remove all ads

#### Solution

$\int2x \sec^3 \left( x^2 + 3 \right) \cdot \tan \left( x^2 + 3 \right) dx$
$= \int \sec^2 \left( x^2 + 3 \right) \cdot \sec \left( x^2 + 3 \right) \cdot \tan \left( x^2 + 3 \right) \cdot \text{2x dx}$
$\text{Let }\sec \left( x^2 + 3 \right) = t$
$\Rightarrow \sec \left( x^2 + 3 \right) \cdot \tan \left( x^2 + 3 \right) \cdot 2x = \frac{dt}{dx}$
$\Rightarrow \sec \left( x^2 + 3 \right) \cdot \tan \left( x^2 + 3 \right) \cdot \text{2x dx} = dt$
$Now, \int \sec^2 \left( x^2 + 3 \right) \cdot \sec \left( x^2 + 3 \right) \cdot \tan \left( x^2 + 3 \right) \cdot \text{2x dx}$
$= \int t^2 dt$
$= \frac{t^3}{3} + C$
$= \frac{\sec^3 \left( x^2 + 3 \right)}{3} + C$

Concept: Indefinite Integral Problems
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.9 | Q 39 | Page 58

#### Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?