Ex 7.4, 21 - Integrate x + 2 / root x2 + 2x + 3 - Ex 7.4

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Ex 7.4, 21 ( + 2)/ ( ^2 + 2 + 3) 1 ( + 2)/ ( ^2 + 2 + 3) =1/2 1 (2 + 4)/ ( ^2 + 2 + 3) =1/2 1 (2 + 2 + 4 2)/ ( ^2 + 2 + 3) =1/2 1 (2 + 2)/ ( ^2 + 2 + 3) +2/2 1 / ( ^2 + 2 + 3) =1/2 1 (2 + 2)/ ( ^2 + 2 + 3) + 1 / ( ^2 + 2 + 3) Solving I1=1/2 1 (2 + 2)/ ( ^2 + 2 + 3) . Let ^2 + 2 + 3= Diff both sides w.r.t.x 2 +2+0= / = /(2 + 2) Now, our equation becomes I1=1/2 1 (2 + 2)/ ( ^2 + 2 + 3) . Putting the value of (4 ^2 ) and I1=1/2 1 (2 + 2)/ . I1=1/2 1 (2 + 2)/ . /(2 + 2) I1=1/2 1 1/ . I1=1/2 1 1/( )^(1/2) . I1=1/2 1 ( )^(( 1)/2) . I1=1/2 ^(( 1)/2 + 1)/(( 1)/2 + 1) + 1 I1= ^(1/2 )+ 1 I1= + 1 I1= ( ^2+2 +3)+ Solving I2= 1 1/ ( ^2 + 2 + 3) . I2= 1 1/ ( ^2 + 2( )(1) + 3) . I2= 1 1/ ( ^2 + 2( )(1) (1)^2 + (1)^2 + 3) . I2= 1 1/ (( + 1)^2 (1)^2 + 3) . I2= 1 1/ (( + 1)^2 1 + 3) . I2= 1 1/ (( + 1)^2 + 2) . I2= 1 1/ (( + 1)^2 +( 2 )^2 ) . I2= 1 1/ ( ^2 + 2( )(1) (1)^2 + (1)^2 + 3) . I2= 1 1/ (( + 1)^2 (1)^2 + 3) . I2= 1 1/ (( + 1)^2 1 + 3) . I2= 1 1/ (( + 1)^2 + 2) . I2= 1 1/ (( + 1)^2 +( 2 )^2 ) . I2= | +1+ (( + 1)^2+( 2 )^2 )|+ 2 I2= | +1+ ( ^2+2 +1+2)|+ 2 I2= | +1+ ( ^2+2 +3)|+ 2 Putting the values of I1 and I2 in (1) 1 ( + 2)/ ( ^2 + 2 + 3). . =1/2 1 (2 + 2)/ ( ^2 + 2 + 3) . + 1 1/ ( ^2 + 2 + 3) . = ( ^2+2 +3)+ 1+ | +1+ ( ^2+2 +3)|+ 2 = ( ^ + + )+ | + + ( ^ + + )|+

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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.