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∫ Tan X Sec 4 X D X - Mathematics

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प्रश्न

` ∫   tan   x   sec^4  x   dx  `

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उत्तर

` ∫   tan   x   sec^4  x   dx  `

= ​∫ tan x. sec2 x . sec^2 x dx

= ∫ tan x (1 + tan^2 x) sec^2 x dx

Let tan x = t

⇒ sec2 x dx = dt 

Now, ∫ tan x (1 + tan2 x) sec2 x dx

= ∫ t (1 + t2) dt

= ∫ (t + t3) dt

\[= \frac{t^2}{2} + \frac{t^4}{4} + C\]
\[ = \frac{1}{2} \tan^2 x + \frac{1}{4} \text{ tan }^4   x + C  \]

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पाठ 19: Indefinite Integrals - Exercise 19.11 [पृष्ठ ६९]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 19 Indefinite Integrals
Exercise 19.11 | Q 2 | पृष्ठ ६९

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