Question 7

Find: ∫ (x 2  + sin 2 โกx) sec 2 โกx / (1 + x 2 ) dx

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Question 7 Find: โˆซ1โ–’((๐‘ฅ^2 + sin^2โก๐‘ฅ ) sec^2โก๐‘ฅ)/(1 + ๐‘ฅ^2 ) dx โˆซ1โ–’((๐‘ฅ^2 + sin^2โก๐‘ฅ ) sec^2โก๐‘ฅ)/(1 + ๐‘ฅ^2 ) dx = โˆซ1โ–’((๐‘ฅ^2 + sin^2โก๐‘ฅ )(1/cos^2โก๐‘ฅ ) )/(1 + ๐‘ฅ^2 ) dx = โˆซ1โ–’((๐‘ฅ^2 + sin^2โก๐‘ฅ ) )/((1 + ๐‘ฅ^2 ) cos^2โก๐‘ฅ ) dx Writing sin2 x = 1 โ€“ cos2 x = โˆซ1โ–’((๐‘ฅ^2 + 1 โˆ’ cos^2โก๐‘ฅ ) )/((1 + ๐‘ฅ^2 ) cos^2โก๐‘ฅ ) dx = โˆซ1โ–’((1 + ๐‘ฅ^2 ) โˆ’ cos^2โก๐‘ฅ )/((1 + ๐‘ฅ^2 ) cos^2โก๐‘ฅ ) dx = โˆซ1โ–’((1 + ๐‘ฅ^2 ) )/((1 + ๐‘ฅ^2 ) cos^2โก๐‘ฅ ) dx โ€“ โˆซ1โ–’(cos^2โก๐‘ฅ )/((1 + ๐‘ฅ^2 ) cos^2โก๐‘ฅ ) dx = โˆซ1โ–’1/cos^2โก๐‘ฅ dx โ€“ โˆซ1โ–’(1 )/((1 + ๐‘ฅ^2 ) ) dx = โˆซ1โ–’ใ€–๐‘ ๐‘’๐‘ใ€—^2โก๐‘ฅ dx โ€“ โˆซ1โ–’(1 )/((1 + ๐‘ฅ^2 ) ) dx = ๐’•๐’‚๐’ ๐’™โˆ’ใ€–๐’•๐’‚๐’ใ€—^(โˆ’๐Ÿ) ๐’™ + 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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.