∫ Sec X Tan X 3 Sec X + 5 D X - Mathematics

Question

\int \frac{\sec x \tan x}{3 \sec x + 5} d x

Sum

Solution

$Let I = \int \frac{s e c x t a n x}{3 \sec x + 5} d x$
$Putting \sec x = t$
$\Rightarrow \frac{d t}{d x} = \sec x \tan x$
$\Rightarrow d t = sec x tan x dx$
$∴ I = \int \frac{d t}{3 t + 5}$
$= \frac{1}{3} ln | 3 t + 5 | + C$
$= \frac{1}{3} ln | 3 \sec x + 5 | + C [∵ t = \sec x]$

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Indefinite Integral Problems

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Q 13 Q 12 Q 14

Chapter 19: Indefinite Integrals - Exercise 19.08 [Page 47]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.08 | Q 13 | Page 47

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∫ Sec X Tan X 3 Sec X + 5 D X - Mathematics

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