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Question 7

Find: ∫ (x 2  + sin 2 ⁑x) sec 2 ⁑x / (1 + x 2 ) dx

Find integral (x^2 + sin^2 x) sec^2 x / (1 + x^2) - Teachoo

Question 7 - CBSE Class 12 Sample Paper for 2019 Boards - Part 2


Transcript

Question 7 Find: ∫1β–’((π‘₯^2 + sin^2⁑π‘₯ ) sec^2⁑π‘₯)/(1 + π‘₯^2 ) dx ∫1β–’((π‘₯^2 + sin^2⁑π‘₯ ) sec^2⁑π‘₯)/(1 + π‘₯^2 ) dx = ∫1β–’((π‘₯^2 + sin^2⁑π‘₯ )(1/cos^2⁑π‘₯ ) )/(1 + π‘₯^2 ) dx = ∫1β–’((π‘₯^2 + sin^2⁑π‘₯ ) )/((1 + π‘₯^2 ) cos^2⁑π‘₯ ) dx Writing sin2 x = 1 – cos2 x = ∫1β–’((π‘₯^2 + 1 βˆ’ cos^2⁑π‘₯ ) )/((1 + π‘₯^2 ) cos^2⁑π‘₯ ) dx = ∫1β–’((1 + π‘₯^2 ) βˆ’ cos^2⁑π‘₯ )/((1 + π‘₯^2 ) cos^2⁑π‘₯ ) dx = ∫1β–’((1 + π‘₯^2 ) )/((1 + π‘₯^2 ) cos^2⁑π‘₯ ) dx – ∫1β–’(cos^2⁑π‘₯ )/((1 + π‘₯^2 ) cos^2⁑π‘₯ ) dx = ∫1β–’1/cos^2⁑π‘₯ dx – ∫1β–’(1 )/((1 + π‘₯^2 ) ) dx = ∫1▒〖𝑠𝑒𝑐〗^2⁑π‘₯ dx – ∫1β–’(1 )/((1 + π‘₯^2 ) ) dx = 𝒕𝒂𝒏 π’™βˆ’γ€–π’•π’‚π’γ€—^(βˆ’πŸ) 𝒙 + C

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.