3 sin x  c u n 1  n / 1 n   n c ∫ Consider (x3 + 3x2 + 6x + 2 )15 (3x2 + 6x + 6) dx The integrand contains the function u = x3 + 3x2 + 6x + 2 and its derivative (3x2 +6x +6) Let u = x3 + 3x2 + 6x + 2 and du = (3x2 + 6x + 6 ) dx (2) Substitution of (1) and (2) in the given integral ∫ (x3 + 3x2 + 6x + 2)15 (3x2 + 6x + 6 )dx =∫ u15 du u 16  16  c  ( 3x2 6x 2)16 c    x3 16  Type 5 ∫sin ∫ u u1 dx form = sin u du = - cos u + c 3 sin ( Consider x 5) (3x 2x) dx.    . 2 2 The integrand contains a function u = x3 + x2 + 5 (within sine) and its derivative u1 = 3x2 + 2x Let u = x3 + x2 + 5 (1) du Then dx = 3x2 + 2x or = (3x2+2x) dx (2) du Substitution of (1) and (2) in the given integral 26 sin (x
3 sin x  c n /  n u n 1 n  1  c Consider ∫ (x3 + 3x2 + 6x + 2 )15 (3x2 + 6x + 6) dx The integrand contains the function u = x3 + 3x2 + 6x + 2 and its derivative (3x2 +6x +6) Let u = x3 + 3x2 + 6x + 2 and du = (3x2 + 6x + 6 ) dx (2) Substitution of (1) and (2) in the given integral ∫ (x3 + 3x2 + 6x + 2)15 (3x2 + 6x + 6 )dx =∫ u15 du  u 16 16  c Type 5 ∫sin u u1 dx form = ∫ sin u du = - cos u + c  ( x3  3x2  6x  2)16 16  c Consider sin 3  x 2  5) (3x 2  2x) dx. . The integrand contains a function u = x3 + x2 + 5 (within sine) and its derivative u1 = 3x2 + 2x Let u = x3 + x2 + 5 (1) Then du dx = 3x2 + 2x or du = (3x2+2x) dx (2) Substitution of (1) and (2) in the given integral 26 sin (x (