急!急!急!求大家幫幫我!!不定積分

1. S (3x + 5)^100 dx

= 1/3 S (3x + 5)^100 d(3x + 5) (Changing variables)

= 1/3 [(3x + 5)^101 / 101] + C

= [(3x + 5)^101] / 303 + C


2. y = (x^3 + 1) / (x - 1)

dy/dx = [(x - 1)(3x^2) - (x^3 + 1)(1)]/(x - 1)^2

= (3x^3 - 3x^2 - x^3 - 1) / (x - 1)^2

= (2x^3 - 3x^2 - 1) / (x - 1)^2


3. lim (x→3) (x^2 - 5x + 6)/(x - 3)

= lim (x→3) (x - 3)(x - 2)/(x - 3)

= lim (x→3) (x - 2)

= 3 - 2

= 1