Question 7
Find: ∫ (x ^{ 2 } + sin ^{ 2 } โกx) sec ^{ 2 } โกx / (1 + x ^{ 2 } ) dx
Last updated at Oct. 1, 2019 by Teachoo
Question 7
Find: ∫ (x ^{ 2 } + sin ^{ 2 } โกx) sec ^{ 2 } โกx / (1 + x ^{ 2 } ) dx
Transcript
Question 7 Find: โซ1โ((๐ฅ^2 + sin^2โก๐ฅ ) sec^2โก๐ฅ)/(1 + ๐ฅ^2 ) dx โซ1โ((๐ฅ^2 + sin^2โก๐ฅ ) sec^2โก๐ฅ)/(1 + ๐ฅ^2 ) dx = โซ1โ((๐ฅ^2 + sin^2โก๐ฅ )(1/cos^2โก๐ฅ ) )/(1 + ๐ฅ^2 ) dx = โซ1โ((๐ฅ^2 + sin^2โก๐ฅ ) )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx Writing sin2 x = 1 โ cos2 x = โซ1โ((๐ฅ^2 + 1 โ cos^2โก๐ฅ ) )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx = โซ1โ((1 + ๐ฅ^2 ) โ cos^2โก๐ฅ )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx = โซ1โ((1 + ๐ฅ^2 ) )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx โ โซ1โ(cos^2โก๐ฅ )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx = โซ1โ1/cos^2โก๐ฅ dx โ โซ1โ(1 )/((1 + ๐ฅ^2 ) ) dx = โซ1โใ๐ ๐๐ใ^2โก๐ฅ dx โ โซ1โ(1 )/((1 + ๐ฅ^2 ) ) dx = ๐๐๐ ๐โใ๐๐๐ใ^(โ๐) ๐ + C
CBSE Class 12 Sample Paper for 2019 Boards
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CBSE Class 12 Sample Paper for 2019 Boards
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