Ex 7.4, 19 - Integrate 6x + 7 / root (x - 5) (x - 4) - Integration by specific formulaes - Method 10

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.4, 19 (6 + 7)/ (( 5)( 4) ) Integrating the function . . . 1 (6 + 7)/ (( 5)( 4) ) . = 1 (6 + 7)/ ( ( 4) 5 ( 4) ) . = 1 (6 + 7)/ ( ^2 4 5 + 20) . = 1 (6 + 7)/ ( ^2 9 + 20) . We can write it as 1 (6 + 7)/ ( ^2 9 + 20) . =6 1 ( + 7/6)/ ( ^2 9 + 20) . =6/2 1 (2 + 14/6)/ ( ^2 9 + 20) . =3 1 (2 9 + 7/3 + 9)/ ( ^2 9 + 20) . =3 1 (2 9 + 34/3)/ ( ^2 9 + 20) . =3 1 (2 9)/ ( ^2 9 + 20) . +3 34/3 1 / ( ^2 9 + 20) =3 1 (2 9)/ (( ^2 9 + 20) ) . +34 1 1/ (( ^2 9 + 20) ) . Solving I1=3 1 (2 9)/ (( ^2 9 + 20) ) . Let ^2 9 +20= Diff both sides w.r.t. x 2 9+0= / = /(2 9) Thus, our equation becomes I1=3 1 (2 9)/ ( ^2 9 + 20) . Put the values of =( ^2 9 +20) and = /(2 9) , we get I1=3 1 (2 9)/ . I1=3 1 (2 9)/ . /(2 9) I1=3 1 1/ . I1=3 1 1/( )^(1/2) . I1=3 1 ( )^(( 1)/2) . I1=3 ^(( 1)/2 + 1)/(( 1)/2 + 1) + 1 I1=3 ^(1/2 )/(1/2) + 1 I1=3 . 2 ^(1/2 )+ 1 I1=6 ^(1/2 )+ 1 I1=6 + 1 I1=6 ( ^2 9 +20)+ 1 Solving , I2=34 1 1/ ( ^2 9 + 20) . I2=34 1 1/ ( ^2 2( )(9/2) + 20) . I2=34 1 1/ ( ^2 2( )(9/2) + (9/2)^2 (9/2)^2+ 20) . I2=34 1 1/ (( 9/2)^2 (9/2)^2+ 20) . I2=34 1 1/ (( 9/2)^2 81/4 + 20) . I2=34 1 1/ (( 9/2)^2 1/4) . I2=34 1 1/ (( 9/2)^2 (1/2)^2 ) . =34[ | 9/2+ (( 9/2)^2+(1/2)^2 )| ]+ 2 =34 | 9/2+ ( ^2+(9/2)^2 2( )(9/2) 1/4) |+ 2 =34 | 9/2+ ( ^2+ 81/4 9 1/4) |+ 2 =34 | 9/2+ ( ^2 9 + 81/4 1/4) |+ 2 =34 | 9/2+ ( ^2 9 + 80/4) |+ 2 =34 | 9/2+ ( ^2 9 +20) |+ 2 Now, putting values of I1 and I2 in eq. 1 1 (6 + 7)/ (( 2)( 4) ) . =3 1 (2 9)/ (( ^2 9 + 20) ) +34 1 1/ (( ^2 9 + 20) ) =6 ( ^2 9 +20)+ 1+34 | 9/2+ ( ^2 9 +20) |+ 2 = ( ^ + ) + | / + ( ^ + ) |+

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