1. 1.
∫ 11 sin 11푥 푑푥 =
11
11
∫ sin 11푥 ∙ 11푑푥
푣 = 11푥 = − cos 11푥 + 퐶
푑푣 = 11푑푥
2.
∫ 11 cos 22푥푑푥 = ∫ cos 11 ∙ 22푑푥
푣 = 22푥
푑푣 = 22푑푥 = 11
22
∫ cos 22푥 ∙ 22푑푥
= 11
22
sin 22푑푥
3.
∫ 11 sec 2 1 푥푑푥 = 11 ∫ 11 sec 2 11푥푑푥
푣 = 1 = 11
11
∫ sec 211푥 ∙ 11푑푥
푑푣 = 1 = 11
11
tan 11푥 + 퐶
4.
∫
22푥푑푥
푒푥 2 = 푒푥 −2
22푥푑푥
푣 = −푥 2 = 22
−22
∫ 푒−푥2
(−22)푥푑푥
푑푣 = −22푥푑푥 = −22
22
푒−푥 2
+ 퐶
=
−1
푒푥 2 + 퐶

2. 5. ∫
55푥2 푑푥
4 푒푥 3 = 55 ∫ 푥 2 푑푥 4 푒−3
= 55 ∫ 푒−푥 3
(4)푥2푑푥
푣 = −푥 3 = 55
4
∫ 푒 푥 3
+ 퐶
푑푣 = −3푥 2푑푥 = 55
4푒푥 3 + 퐶
6. ∫(11) 2 푥 ∙ sec 푥2 ∙ tan 푥2 푑푥 = ∫ 121 푥 ∙ sec 푥2 ∙ tan 푥2 푑푥
푣 = 푥 2 = 121
2
∫ sec 푥 2 ∙ tan 푥 2 2푥푑푥
푑푣 = 2푥푑푥 = 121
2
sec 푥 2 + 퐶
7. ∫(11) 2 ∙ csc 2 푥 3푑푥 = ∫ 121푥 2 − csc 2 푥 3푑푥
푣 = 푥 3 = 121
3
∫ csc 2 푥 3 3푥 2푑푥
푑푣 = 3푥 2 푑푥 = 121
3
− cot 푥 3 + 퐶
8. 11푥2푒푥 푒
푑푥 = ∫ 11푥 2 + ∫ 푒푥 3
− 푑푥
= 11 (
푥 2+1
2 + 1
) +
푒푥 3+1
푥 3 + 1
+ 퐶
= 11 (푥 3
3
) + 푒푥 3
푥 3 + 퐶
= 11푥 3
3
+ 푒 푥 3
푥3 + 퐶
9. ∫ 11푥 3 csc 푥 4 ∙ cot 푥 4 = ∫ 11푥 3 csc 푥 4 ∙ cot 푥 4푑푥
=
11
4
csc 푥 4 cot 푥 4 4푥 3 푑푥
=
11
4
∙ csc 푥 4 + 퐶

3. 10. ∫ 11푥2 푑푥
√16−푥6 = 1
3
∫
33 푥2 푑푥
√16 −푥6
푎2 = 16 푑 = 14 = 1
3
푎푟푐 sin 푥3
4
+ 퐶
푣2 = 푥 6 푣 = 푥 3
푑푣 = 3푥 2푑푥