展開する sec(t)(5sec(t)+3tan(t))dt

解

展開する

sec (t) (5 sec (t) + 3 tan (t)) d t

5 sec^{2} (t) d t + 3 sec (t) tan (t) d t

解答ステップ

sec (t) (5 sec (t) + 3 tan (t)) d t

分配法則を適用する:

a (b + c) = ab + a c

a = sec (t) d t, b = 5 sec (t), c = 3 tan (t)

= sec (t) d t \cdot 5 sec (t) + sec (t) d t \cdot 3 tan (t)

= 5 sec (t) sec (t) d t + 3 sec (t) tan (t) d t

5 sec (t) sec (t) d t = 5 sec^{2} (t) d t

= 5 sec^{2} (t) d t + 3 sec (t) tan (t) d t