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Latihan integral parsial • 1. INTEGRAL PARSIAL • 1 6 ( x + 2) 6 6 1 1 ( x + 2) 6 ( x + 2) 6.6 6 6 1 x( x + 2 ) 6 ( x + 2) 7 7 Bila dilanjutnya, bentuk penyelesaiannya menjadi:  7x − x − 2 = ( x + 2) ( x − ( x + 2)) + C = ( x + 2)  6 1 7 6 +C  7 = 1 ( x + 2) 6 (6 x − 2) + C = 7 ( x + 2) 6 (3 x − 1) + C 7 2 • Soal Nomor 2. ∫ 2 x (3 x − 2) 6 dx = u = 2x dv = (3x – 5)6 du= 2 v= 1 (3x − 5)7 21 ∫u dv = ∫ uv − v du 1 1 2 x (3 x − 5) − ∫ (3 x − 5) 7.2 ∫ 2x 7 (3 x − 5) dx = 6 21 21 2x 2 2x 1= (3x − 5) − 7 = (3x − 5) + C 21 8 (3x − 5) − 7 (3x − 5)8 + C 21 21.3.8 252  2x 1  7  2x 3x 5 = (3x − 5)  − 7.(3x − 5)  + C = (3x − 5)  − + +C  21 252   21 252 252   12 x 5  1= (3 x − 5) 7 +  +C = (3x − 5) (12 x + 5) + C 7  252 252  252 • Soal Nomor 3 ∫ 4x 3 x − 2dx = 1 u = 4x dv = (3 x − 2) 2 2 5 du = 4 v= (3 x − 2) 2 9 2 2 8 8 1 2= 4 x (3 x − 2) − ∫ (3 x − 2) 2.4dx 1 3 3 5 2 = x(3 x − 2) −.. (3 x − 2) 2 + C 2 9 9 9 9 3 5 8 3  2  8 3 15 x − 2(3 x − 2) = (3 x − 2) 2  x − (3 x − 2) + C = (3 x − 2) 2  +C 9  15  9  15  8 3  9 x + 4)  8 3 15 x − 6 x + 4) = (3 x − 2) 2  = (3x − 2) 2  +C 9 15 +C 9  15    8 3 = (3 x − 2) 2 (9 x + 4) + C 135 • dv = ( 3 x − 1) −1 Soal Nomor 4 u = 6x 3 1 −Hasil dari ∫ 6 x(3 x − 1) dx = (UN 2005) 3 du = 6 1 v = ( 3x - 1) 3 2 1 2 − ∫ 6 x(3x −1) dx =6 x. (3 x −1) − ∫ (3 x −1).6dx 2 2 3 1 3 1 3 2 2 1 − 1 3 ∫ 6 x(3x −1) 2 5 dx =3 x(3 x −1) 3 − 3.. (3 x −1) 3 + C 3 3 5 1 − 3 ∫ 2 5 6 x (3 x −1) dx =3 x(3 x −1) − (3 x −1) 3 + C 3 3 5 Jika penyelesaian ini dilanjukan, maka bentuknya menjadi 1 − 3 ∫ 6 x(3x −1) dx =( 3 x −1) (3 x − (3 x −1) + C 2 3 3 5 1 − 2  15 x − 9 x + 3  ∫ 6 x (3 x −1) dx =( 3 x −1) 3  3  +C  15  1 − (6 x + 3) ∫ 6 x(3x −1) dx =( 3 x −1) 2 3 3 +C 15 1 − 1 ∫ 6 x(3x −1) dx = ( 3 x −1) 3 ( 2 x +1) + C 2 3 5 • dv = ( 3- 2 x ) Hasil dari 1 u =x 2∫ x 3 − 2 x dx = (UAN,2004; No.

33) du = dx v =−. 1 2 (3 − 2 x ) 2 3 3 2 = − 1 (3 − 2 x ) 3 2 3∫x 3 − 2 x dx = x.