Question

当x→0时,ln（1+ax）与sin3x等价,则常数a= 计算 ∫（x+1)^2dx

Answer 1

lim(x→0) ln(1 + ax)/sin3x

= lim(x→0) [a/(1 + ax)]/[3cos3x]

= [a/(1 + 0)]/[3(1)]

= a/3

==> a = 3

∫ (x + 1)² dx

= ∫ (x + 1)² d(x + 1)

= (x² + 1)³/3 + C