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TUGAS 3
NAMA KELOMPOK : 1.SUSANDI 2.RAFIS 3.GERIAN
KELAS : 1EA
LATIHAN 7.1
1. ∫ 100 𝑑𝑥 = 100𝑥 + 𝑐
2. ∫ 6𝑥 𝑑𝑥 = 3𝑥2
+ 𝑐
3. ∫( 3𝑥2
+ 4𝑥 − 5) 𝑑𝑥 = 𝑥3
+ 2𝑥 −
5𝑥 + 𝑐
4. ∫( 𝑥2
+ 1)√ 𝑥 𝑑𝑥 =
2
7
𝑥2
1
+
2
3
𝑥2
3
+ 𝑐
5. ∫( 𝑥 𝑒
+ 𝑒 𝑥 ) 𝑑𝑥 =
𝑥 𝑒+1
𝑒+1
+ 𝑒 𝑥
+ 𝑐
6. ∫(10𝑥 + 30)3
10 𝑑𝑥 =
(10𝑥+30)4
4
+ 𝑐
7. ∫(𝑥2
− 3)4
2𝑥 𝑑𝑥 =
(𝑥2−3)5
5
+ 𝑐
8. ∫(𝑠𝑖𝑛2
𝑥cos 𝑥) 𝑑𝑥 =
𝑠𝑖𝑛3
3
𝑥 + 𝑐
9. ∫ 𝑥2
− 𝑠𝑖𝑛 𝑥3
𝑑𝑥 =
− cos 𝑥3
3
+ 𝑐
10. ∫ 𝐼𝑛 𝑥 𝑑𝑥 = 𝑥 𝐼𝑛 𝑥 = 𝑥 𝐼𝑛 𝑥 − 𝑥 +
𝑐
penyelesaian :
1. =
𝑑
𝑑𝑥
(100𝑥 + 𝑐) = 100𝑥 + 𝑐
2. =
𝑑
𝑑𝑥
(3𝑥2
+ 𝑐) = 6𝑥 + 0 = 100
3. =
𝑑
𝑑𝑥
(𝑥3
+ 2𝑥2
− 5𝑥 + 𝑐) = 3𝑥2
+ 4𝑥 − 5 + 0 = 3𝑥2
+4x-5
4. =
𝑑
𝑑𝑥
(
2𝑥
1
2
7
+
2𝑥
3
2
3
+ c)=
2𝑥
−1
2
14
+
6𝑥
1
2
6
+ 0 =
1𝑥
−1
2
7
+ 𝑥
1
2
5. =
𝑑
𝑑𝑥
(
𝑥 𝑒+1
𝑒+1
+ 𝑒 𝑥
+ 𝑐) =
𝑒+1.𝑥 𝑒+1−1
1𝑒1−1+0
+ 𝑥𝑒 𝑥−1
+ 𝑐 =
𝑒+𝑥 𝑒
1
+ 𝑥𝑒 𝑥−1
+ 0 = 𝑒 + 𝑥 𝑒
+
𝑥𝑒 𝑥−1
6. =
𝑑
𝑑𝑥
(10𝑥+30)4
4
+ 𝑐 =
10𝑥4
4
+
304
4
+ 𝑐 =
40𝑥3
4
+ 0 = 10𝑥3
7. =
𝑑
𝑑𝑥
(𝑥2−3)5
5
+ c =
𝑥10
5
−
35
5
+ 𝑐 =
10𝑥9
5
+ 0 = 2𝑥9
8. =
𝑑
𝑑𝑥
(
𝑠𝑖𝑛3
3
𝑥 + 𝑐) =
𝑠𝑖𝑛2 𝑥
3
.
sin 𝑥
3
+ 0 =
(1−𝑐𝑜𝑠2 𝑥) .
3
sin 𝑥
3
9. =
𝑑
𝑑𝑥
(
− cos 𝑥3
3
+ 𝑐) =
−3 sin 𝑥2
3
+ 0 = −sin 𝑥2
10. =
𝑑
𝑑𝑥
( 𝑥 𝐼𝑛 𝑥 − 𝑥 + 𝑐) = 𝑥.
𝑑𝑥
𝑥
− 1 =
𝑥−1𝑑𝑥
𝑥
LATIHAN 7.2
1. ∫8 𝑑𝑥
2. ∫
3
4
𝑑𝑥
3. ∫9.75 𝑑𝑥
4. ∫√3𝑑𝑥
5. ∫(
√40
3
√10+15
)𝑑𝑥
6. ∫16 √2 𝑑𝑡
7. ∫ 𝑒2
𝑑𝑥
8. ∫2𝜋 𝑑𝑟
9. ∫−21𝑑𝑢
10.∫
6
𝑒
𝑑𝑥
Penyelesaian :
1. = 8x+c
2. =
3
4
𝑥 + 𝑐
3. = 9𝑥. 75𝑥 + 𝑐
4. = √3 x+c
5. =
40𝑥
2
3
10𝑥
1
2+15𝑥
+ 𝑐
6. = 16𝑡. √2 𝑡 + c
7. = 𝑒𝑥2
+ c
8. = 2𝑟. 𝜋𝑟 + c
9. = -21 u + c
10.=
6𝑥
𝑒𝑥
+ c
LATIHAN 7.3
1. ∫ 𝑥5
𝑑𝑥
2. ∫ √ 𝑥34
𝑑𝑥
3. ∫ 𝑥√2
𝑑𝑥
4. ∫
1
𝑥2
𝑑𝑥
5. ∫ 𝑡100
𝑑𝑡
6. ∫ 𝑢2𝜋
𝑑𝑢
7. ∫
1
√𝑥
𝑑𝑥
8. ∫
𝑥5
𝑥2
𝑑𝑥
9. ∫ 𝑟−1
𝑑𝑟
10.∫
1
𝑡
𝑑𝑡
Penyelesaian :
1. =
𝑥6
6
+ 𝑐
2. = ∫ 𝑥
3
4 𝑑𝑥 =
𝑥
7
4
7
4
+ c =
4𝑥
7
4
7
+ 𝑐
3. =
𝑥√2+1
√2+1
+ 𝑐
4. =∫ 𝑥−2
𝑑𝑥 =
𝑥−1
−1
+ 𝑐 = −
1
𝑥
+ 𝑐
5. =
𝑡101
101
+ 𝑐
6. =
42𝜋+1
2𝜋+1
+ 𝑐
7. = ∫ 𝑥
−1
2 𝑑𝑥 =
𝑥
1
2
1
2
+ 𝑐 =
2𝑥
1
2
1
+ 𝑐
8. =
𝑥6
𝑥3
+ 𝑐
9. =
𝑟−1+1
−1+1
+ 𝑐 = ∞
10.∫ 𝑡−1
𝑑𝑡 =
𝑡−1+1
−1+1
+ 𝑐 = ∞
LATIHAN 7.4
1. ∫ 𝑒 𝑡
𝑑𝑡
2. ∫ 𝑒20𝑥
𝑑𝑥
3. ∫ 𝑒 𝜋𝑥
𝑑𝑥
4. ∫ 𝑒0,25𝑥
𝑑𝑥
5. ∫ 𝑒
𝑥
5 𝑑𝑥
6. ∫ 𝑒√3𝑥
𝑑𝑥
7. ∫4 𝑥
𝑑𝑥
8. ∫23𝑥
𝑑𝑥
9. ∫1000,25𝑥
𝑑𝑥
10.∫ 𝜋
𝑥
5 𝑑𝑥
Penyelesaian :
1. = 𝑒 𝑡
+ 𝑐
2. =
1
20
𝑒20𝑥
+ 𝑐 =
𝑒20𝑥
5
+ 𝑐
3. =
1
𝜋
𝑒 𝜋𝑥
+ 𝑐 =
𝑒 𝜋𝑥
𝜋
+ 𝑐
4. =
1
0,25
𝑒0,25𝑥
+ 𝑐 =
𝑒0,25𝑥
0,25
+ 𝑐
5. =
1
𝑥
5
𝑒
𝑥
5 + 𝑐 =
5
𝑥
𝑒
𝑥
5 + 𝑐
6. =
1
√3
𝑒√3𝑥
+ 𝑐 =
𝑒√3𝑥
√3
+ c
7. =
1
𝐼𝑛 4
4 𝑥
+ 𝑐 =
4 𝑥
𝐼𝑛 4
+ 𝑐
8. =
1
3 𝐼𝑛 2
23𝑥
+ 𝑐 =
23𝑥
3 𝐼𝑛 2
+ 𝑐
9. =
1
0,25 𝐼𝑛 100
1000,25𝑥
+ 𝑐 =
1000,25𝑥
0,25 𝐼𝑛 100
+ 𝑐
10.=
1
𝑥
5
𝜋
𝑥
5 + 𝑐 =
5
𝑥
𝜋
𝑥
5 + 𝑐
LATIHAN 7.5
1. ∫cos 𝑣 𝑑𝑣
2. ∫sin(
1
2
𝜋𝑥)𝑑𝑥
3. ∫cos(18) 𝑑𝑥
4. ∫ 𝑠𝑒𝑐2
(√3𝑥)𝑑𝑥
5. ∫ 𝑐𝑠𝑐2
(2,5) 𝑑𝑥
6. ∫sec (
5
6
𝑥)tan(
5
6
𝑥)𝑑𝑥
7. ∫csc
x
3
𝑐𝑜𝑡
𝑥
3
𝑑𝑥
8. ∫csc(ex) cot(𝑒𝑥)𝑑𝑥
9. ∫sin 3𝜃 𝑑𝜃
10.∫cos(25𝜋𝑥) 𝑑𝑥
Penyelesaian :
1. = Sin v + c
2. = −
1
1
2𝜋
cos (
1
2
𝜋𝑥) + 𝑐 = −2𝜋cos (
1
2
𝜋𝑥) + 𝑐
3. =
1
8
sin(18𝑥) + 𝑐
4. =
1
√3
tan(√3𝑥) + 𝑐 =
tan(√3𝑥)
√3
+ 𝑐
5. = −
1
2,5
cot(2,5 𝑥) + 𝑐 =
−cot(2,5𝑥)
2,5
+ 𝑐
6. =
1
5
6
sec(
5
6
𝑥) + 𝑐 =
6
5
sec (
5
6
𝑥) + 𝑐
7. =
1
1
3
csc(
x
3
) + c = 3 csc (
𝑥
3
) + 𝑐
8. = −
1
𝑒
csc (ex) + c =
− csc( 𝑒𝑥)
𝑒
+ 𝑐
9. = −
1
3
cos(3𝜃) + 𝑐 =
−cos(3𝜃)
3
+ c
10.=
1
25𝜋
sin(25𝜋𝑥) + 𝑐 =
sin(25 𝜋𝑥)
25𝜋
+ c
LATIHAN 7.6
1. ∫
1
1+𝜃2
𝑑𝜃
2. ∫
𝑑𝑥
√16−𝑥2
3. ∫
1
49+𝑥2
𝑑𝑥
4. ∫
𝑑𝑡
0,25+𝑡2
5. ∫
𝑑𝑢
√𝑢2(𝑢2−1)
6. ∫
1
|𝑥|√𝑥2−41
𝑑𝑥
7. ∫
1
√
81
100
−𝑥2
𝑑𝑥
8. ∫
1
𝜋2+𝑥2
𝑑𝑥
9. ∫
𝑑𝑡
√𝑡2(𝑡2−
1
4
)
10.∫
1
|𝑥|√𝑥2−7
𝑑𝑥
Penyelesaian :
1. = 𝑡𝑎𝑛−1
𝜃 + 𝑐 = −𝑐𝑜𝑡−1
𝜃 + 𝑐
2. = ∫
1
√42−√𝑥2
𝑑𝑥 = 𝑠𝑖𝑛−1
(
𝑥
4
) + 𝑐
3. = ∫
1
√492+𝑥2
𝑑𝑥 =
1
√49
𝑡𝑎𝑛−1
(
𝑥
√49
) + 𝑐
4. = ∫
1
√0,252+𝑡2
𝑑𝑡 =
1
√0,25
𝑡𝑎𝑛−1
(
𝑡
√0,25
)+ 𝑐
5. = ∫
1
|𝑢|√𝑢2−√12
𝑑𝑢 =
1
1
𝑠𝑒𝑐−1
(
𝑢
1
) + 𝑐 = 𝑠𝑒𝑐−1( 𝑢) + 𝑐
6. = 𝑠𝑒𝑐−1
(
𝑥
41
) + c = - 𝑐𝑠𝑐−1
(
𝑥
41
) + c
7. = ∫
1
√
(9)2
10
−𝑥2
𝑑𝑥 = 𝑠𝑖𝑛−1
(
𝑥
9
10
) + 𝑐 =𝑠𝑖𝑛−1
(
10𝑥
9
) + 𝑐 = −𝑐𝑜𝑠−1
(
10𝑥
9
) + 𝑐
8.
1
𝜋
𝑡𝑎𝑛−1 𝑥
𝜋
+ 𝑐 = −
1
𝜋
𝑐𝑜𝑡−1
(
𝑥
𝜋
)+c
9.= ∫
1
| 𝑡|√ 𝑡2−
(1)
2
2
𝑑𝑥 =
1
1
2
𝑠𝑒𝑐−1
(
𝑡
1
2
) + 𝑐 = 2𝑠𝑒𝑐−1(2𝑡) + 𝑐
10.𝑠𝑒𝑐−1
(
𝑥
7
) + 𝑐 = −𝑐𝑠𝑐−1
(
𝑥
7
) + 𝑐

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Tugas 3

  • 1. TUGAS 3 NAMA KELOMPOK : 1.SUSANDI 2.RAFIS 3.GERIAN KELAS : 1EA LATIHAN 7.1 1. ∫ 100 𝑑𝑥 = 100𝑥 + 𝑐 2. ∫ 6𝑥 𝑑𝑥 = 3𝑥2 + 𝑐 3. ∫( 3𝑥2 + 4𝑥 − 5) 𝑑𝑥 = 𝑥3 + 2𝑥 − 5𝑥 + 𝑐 4. ∫( 𝑥2 + 1)√ 𝑥 𝑑𝑥 = 2 7 𝑥2 1 + 2 3 𝑥2 3 + 𝑐 5. ∫( 𝑥 𝑒 + 𝑒 𝑥 ) 𝑑𝑥 = 𝑥 𝑒+1 𝑒+1 + 𝑒 𝑥 + 𝑐 6. ∫(10𝑥 + 30)3 10 𝑑𝑥 = (10𝑥+30)4 4 + 𝑐 7. ∫(𝑥2 − 3)4 2𝑥 𝑑𝑥 = (𝑥2−3)5 5 + 𝑐 8. ∫(𝑠𝑖𝑛2 𝑥cos 𝑥) 𝑑𝑥 = 𝑠𝑖𝑛3 3 𝑥 + 𝑐 9. ∫ 𝑥2 − 𝑠𝑖𝑛 𝑥3 𝑑𝑥 = − cos 𝑥3 3 + 𝑐 10. ∫ 𝐼𝑛 𝑥 𝑑𝑥 = 𝑥 𝐼𝑛 𝑥 = 𝑥 𝐼𝑛 𝑥 − 𝑥 + 𝑐 penyelesaian : 1. = 𝑑 𝑑𝑥 (100𝑥 + 𝑐) = 100𝑥 + 𝑐 2. = 𝑑 𝑑𝑥 (3𝑥2 + 𝑐) = 6𝑥 + 0 = 100 3. = 𝑑 𝑑𝑥 (𝑥3 + 2𝑥2 − 5𝑥 + 𝑐) = 3𝑥2 + 4𝑥 − 5 + 0 = 3𝑥2 +4x-5 4. = 𝑑 𝑑𝑥 ( 2𝑥 1 2 7 + 2𝑥 3 2 3 + c)= 2𝑥 −1 2 14 + 6𝑥 1 2 6 + 0 = 1𝑥 −1 2 7 + 𝑥 1 2 5. = 𝑑 𝑑𝑥 ( 𝑥 𝑒+1 𝑒+1 + 𝑒 𝑥 + 𝑐) = 𝑒+1.𝑥 𝑒+1−1 1𝑒1−1+0 + 𝑥𝑒 𝑥−1 + 𝑐 = 𝑒+𝑥 𝑒 1 + 𝑥𝑒 𝑥−1 + 0 = 𝑒 + 𝑥 𝑒 + 𝑥𝑒 𝑥−1 6. = 𝑑 𝑑𝑥 (10𝑥+30)4 4 + 𝑐 = 10𝑥4 4 + 304 4 + 𝑐 = 40𝑥3 4 + 0 = 10𝑥3 7. = 𝑑 𝑑𝑥 (𝑥2−3)5 5 + c = 𝑥10 5 − 35 5 + 𝑐 = 10𝑥9 5 + 0 = 2𝑥9 8. = 𝑑 𝑑𝑥 ( 𝑠𝑖𝑛3 3 𝑥 + 𝑐) = 𝑠𝑖𝑛2 𝑥 3 . sin 𝑥 3 + 0 = (1−𝑐𝑜𝑠2 𝑥) . 3 sin 𝑥 3 9. = 𝑑 𝑑𝑥 ( − cos 𝑥3 3 + 𝑐) = −3 sin 𝑥2 3 + 0 = −sin 𝑥2 10. = 𝑑 𝑑𝑥 ( 𝑥 𝐼𝑛 𝑥 − 𝑥 + 𝑐) = 𝑥. 𝑑𝑥 𝑥 − 1 = 𝑥−1𝑑𝑥 𝑥
  • 2. LATIHAN 7.2 1. ∫8 𝑑𝑥 2. ∫ 3 4 𝑑𝑥 3. ∫9.75 𝑑𝑥 4. ∫√3𝑑𝑥 5. ∫( √40 3 √10+15 )𝑑𝑥 6. ∫16 √2 𝑑𝑡 7. ∫ 𝑒2 𝑑𝑥 8. ∫2𝜋 𝑑𝑟 9. ∫−21𝑑𝑢 10.∫ 6 𝑒 𝑑𝑥 Penyelesaian : 1. = 8x+c 2. = 3 4 𝑥 + 𝑐 3. = 9𝑥. 75𝑥 + 𝑐 4. = √3 x+c 5. = 40𝑥 2 3 10𝑥 1 2+15𝑥 + 𝑐 6. = 16𝑡. √2 𝑡 + c 7. = 𝑒𝑥2 + c 8. = 2𝑟. 𝜋𝑟 + c 9. = -21 u + c 10.= 6𝑥 𝑒𝑥 + c
  • 3. LATIHAN 7.3 1. ∫ 𝑥5 𝑑𝑥 2. ∫ √ 𝑥34 𝑑𝑥 3. ∫ 𝑥√2 𝑑𝑥 4. ∫ 1 𝑥2 𝑑𝑥 5. ∫ 𝑡100 𝑑𝑡 6. ∫ 𝑢2𝜋 𝑑𝑢 7. ∫ 1 √𝑥 𝑑𝑥 8. ∫ 𝑥5 𝑥2 𝑑𝑥 9. ∫ 𝑟−1 𝑑𝑟 10.∫ 1 𝑡 𝑑𝑡 Penyelesaian : 1. = 𝑥6 6 + 𝑐 2. = ∫ 𝑥 3 4 𝑑𝑥 = 𝑥 7 4 7 4 + c = 4𝑥 7 4 7 + 𝑐 3. = 𝑥√2+1 √2+1 + 𝑐 4. =∫ 𝑥−2 𝑑𝑥 = 𝑥−1 −1 + 𝑐 = − 1 𝑥 + 𝑐 5. = 𝑡101 101 + 𝑐 6. = 42𝜋+1 2𝜋+1 + 𝑐 7. = ∫ 𝑥 −1 2 𝑑𝑥 = 𝑥 1 2 1 2 + 𝑐 = 2𝑥 1 2 1 + 𝑐 8. = 𝑥6 𝑥3 + 𝑐 9. = 𝑟−1+1 −1+1 + 𝑐 = ∞
  • 4. 10.∫ 𝑡−1 𝑑𝑡 = 𝑡−1+1 −1+1 + 𝑐 = ∞ LATIHAN 7.4 1. ∫ 𝑒 𝑡 𝑑𝑡 2. ∫ 𝑒20𝑥 𝑑𝑥 3. ∫ 𝑒 𝜋𝑥 𝑑𝑥 4. ∫ 𝑒0,25𝑥 𝑑𝑥 5. ∫ 𝑒 𝑥 5 𝑑𝑥 6. ∫ 𝑒√3𝑥 𝑑𝑥 7. ∫4 𝑥 𝑑𝑥 8. ∫23𝑥 𝑑𝑥 9. ∫1000,25𝑥 𝑑𝑥 10.∫ 𝜋 𝑥 5 𝑑𝑥 Penyelesaian : 1. = 𝑒 𝑡 + 𝑐 2. = 1 20 𝑒20𝑥 + 𝑐 = 𝑒20𝑥 5 + 𝑐 3. = 1 𝜋 𝑒 𝜋𝑥 + 𝑐 = 𝑒 𝜋𝑥 𝜋 + 𝑐 4. = 1 0,25 𝑒0,25𝑥 + 𝑐 = 𝑒0,25𝑥 0,25 + 𝑐 5. = 1 𝑥 5 𝑒 𝑥 5 + 𝑐 = 5 𝑥 𝑒 𝑥 5 + 𝑐 6. = 1 √3 𝑒√3𝑥 + 𝑐 = 𝑒√3𝑥 √3 + c 7. = 1 𝐼𝑛 4 4 𝑥 + 𝑐 = 4 𝑥 𝐼𝑛 4 + 𝑐 8. = 1 3 𝐼𝑛 2 23𝑥 + 𝑐 = 23𝑥 3 𝐼𝑛 2 + 𝑐 9. = 1 0,25 𝐼𝑛 100 1000,25𝑥 + 𝑐 = 1000,25𝑥 0,25 𝐼𝑛 100 + 𝑐 10.= 1 𝑥 5 𝜋 𝑥 5 + 𝑐 = 5 𝑥 𝜋 𝑥 5 + 𝑐
  • 5. LATIHAN 7.5 1. ∫cos 𝑣 𝑑𝑣 2. ∫sin( 1 2 𝜋𝑥)𝑑𝑥 3. ∫cos(18) 𝑑𝑥 4. ∫ 𝑠𝑒𝑐2 (√3𝑥)𝑑𝑥 5. ∫ 𝑐𝑠𝑐2 (2,5) 𝑑𝑥 6. ∫sec ( 5 6 𝑥)tan( 5 6 𝑥)𝑑𝑥 7. ∫csc x 3 𝑐𝑜𝑡 𝑥 3 𝑑𝑥 8. ∫csc(ex) cot(𝑒𝑥)𝑑𝑥 9. ∫sin 3𝜃 𝑑𝜃 10.∫cos(25𝜋𝑥) 𝑑𝑥 Penyelesaian : 1. = Sin v + c 2. = − 1 1 2𝜋 cos ( 1 2 𝜋𝑥) + 𝑐 = −2𝜋cos ( 1 2 𝜋𝑥) + 𝑐 3. = 1 8 sin(18𝑥) + 𝑐 4. = 1 √3 tan(√3𝑥) + 𝑐 = tan(√3𝑥) √3 + 𝑐 5. = − 1 2,5 cot(2,5 𝑥) + 𝑐 = −cot(2,5𝑥) 2,5 + 𝑐 6. = 1 5 6 sec( 5 6 𝑥) + 𝑐 = 6 5 sec ( 5 6 𝑥) + 𝑐 7. = 1 1 3 csc( x 3 ) + c = 3 csc ( 𝑥 3 ) + 𝑐 8. = − 1 𝑒 csc (ex) + c = − csc( 𝑒𝑥) 𝑒 + 𝑐 9. = − 1 3 cos(3𝜃) + 𝑐 = −cos(3𝜃) 3 + c 10.= 1 25𝜋 sin(25𝜋𝑥) + 𝑐 = sin(25 𝜋𝑥) 25𝜋 + c
  • 6. LATIHAN 7.6 1. ∫ 1 1+𝜃2 𝑑𝜃 2. ∫ 𝑑𝑥 √16−𝑥2 3. ∫ 1 49+𝑥2 𝑑𝑥 4. ∫ 𝑑𝑡 0,25+𝑡2 5. ∫ 𝑑𝑢 √𝑢2(𝑢2−1) 6. ∫ 1 |𝑥|√𝑥2−41 𝑑𝑥 7. ∫ 1 √ 81 100 −𝑥2 𝑑𝑥 8. ∫ 1 𝜋2+𝑥2 𝑑𝑥 9. ∫ 𝑑𝑡 √𝑡2(𝑡2− 1 4 ) 10.∫ 1 |𝑥|√𝑥2−7 𝑑𝑥 Penyelesaian : 1. = 𝑡𝑎𝑛−1 𝜃 + 𝑐 = −𝑐𝑜𝑡−1 𝜃 + 𝑐 2. = ∫ 1 √42−√𝑥2 𝑑𝑥 = 𝑠𝑖𝑛−1 ( 𝑥 4 ) + 𝑐 3. = ∫ 1 √492+𝑥2 𝑑𝑥 = 1 √49 𝑡𝑎𝑛−1 ( 𝑥 √49 ) + 𝑐 4. = ∫ 1 √0,252+𝑡2 𝑑𝑡 = 1 √0,25 𝑡𝑎𝑛−1 ( 𝑡 √0,25 )+ 𝑐 5. = ∫ 1 |𝑢|√𝑢2−√12 𝑑𝑢 = 1 1 𝑠𝑒𝑐−1 ( 𝑢 1 ) + 𝑐 = 𝑠𝑒𝑐−1( 𝑢) + 𝑐 6. = 𝑠𝑒𝑐−1 ( 𝑥 41 ) + c = - 𝑐𝑠𝑐−1 ( 𝑥 41 ) + c 7. = ∫ 1 √ (9)2 10 −𝑥2 𝑑𝑥 = 𝑠𝑖𝑛−1 ( 𝑥 9 10 ) + 𝑐 =𝑠𝑖𝑛−1 ( 10𝑥 9 ) + 𝑐 = −𝑐𝑜𝑠−1 ( 10𝑥 9 ) + 𝑐 8. 1 𝜋 𝑡𝑎𝑛−1 𝑥 𝜋 + 𝑐 = − 1 𝜋 𝑐𝑜𝑡−1 ( 𝑥 𝜋 )+c
  • 7. 9.= ∫ 1 | 𝑡|√ 𝑡2− (1) 2 2 𝑑𝑥 = 1 1 2 𝑠𝑒𝑐−1 ( 𝑡 1 2 ) + 𝑐 = 2𝑠𝑒𝑐−1(2𝑡) + 𝑐 10.𝑠𝑒𝑐−1 ( 𝑥 7 ) + 𝑐 = −𝑐𝑠𝑐−1 ( 𝑥 7 ) + 𝑐