24 2  (using the Basic formula we have)  9  c = 1 +c -9u 9   e c u  1 3 Type 3  c ∫eu dx = e du u x 3  sin x e Consider ∫ (3x cos x )  dx 2 The integrand contains the function u = x3 + sin x and its derivative (3x2 + cos x) Let u = x3 + sin x (1) du dx = 3x2 + cos x Then du = (3x2 + cosx) dx (2) Substitution of (1) and (2) in the given integral x e 2 (3x cos x )  dx 3 sin x    e c using the basic formula u 25 u  e x
24 2  (using the Basic formula we have)  9  c = 1 +c -9u 9  Type 3 ∫eu dx = e u du 1 3  e u  c  c Consider e x 3  sin x (3x 2  cos x ) dx ∫ The integrand contains the function u = x3 + sin x and its derivative (3x2 + cos x) Let u = x3 + sin x (1) du dx = 3x2 + cos x Then du = (3x2 + cosx) dx (2) Substitution of (1) and (2) in the given integral e x 3  sin x (3x 2  cos x ) dx using the basic formula u  e u  c 25  e x
CALCULUS%20II.DOCX