Exercise 3.3
Exercise 3.3
Exercise 3.3
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MA111: Prepared by Dr.Archara Pacheenburawana 48<br />
17.<br />
∫<br />
e t√ 9−e 2t dt 18.<br />
∫<br />
dx<br />
√<br />
x2 +a 2 dx<br />
Answer to <strong>Exercise</strong> 6.3<br />
√<br />
π<br />
1. + √ 3<br />
− 1 2. − 4−x2 25−x<br />
24 8 4<br />
2x +C 3. − 2<br />
25x<br />
+C 4. ( √ 1 3<br />
)ln<br />
∣<br />
1<br />
5.<br />
3 (x2 +4) 3/2 −4 √ x 2 +4+C 6. 1 4 sin−1 (2x)+ 1x√ 1−4x<br />
2 2 +C<br />
√ 1<br />
7. x√ x<br />
2 2 x<br />
+4+2ln<br />
∣2 + x2 +4<br />
2 ∣ +C 8. √ 9x 2 −4−2sec −1 ( 3x )+C 2<br />
( √ x 2 +3− √ 3)<br />
x<br />
∣ +C<br />
9.<br />
13.<br />
15.<br />
x<br />
√<br />
a2 −x 2 −sin−1( x<br />
a)<br />
+C 10.<br />
√<br />
x2 −7+C 11. ln(1+ √ 2) 12. 1 3 (x2 +4) 3/2 +C<br />
64<br />
1215<br />
14. 1 2 [sin−1 (x−1)+(x−1) √ 2x−x 2 ]+C<br />
1<br />
ln∣ √<br />
∣<br />
3 3x+1+ 9x2 +6x−8 ∣ +C 16.<br />
1<br />
2<br />
[<br />
tan −1 (x−1)+<br />
]<br />
(x+1)<br />
+C<br />
(x 2 +2x+2)<br />
[<br />
1<br />
17. √ 2 e<br />
t<br />
9−e 2t +9sin −1 ( et)]<br />
+C 18. ln(x+ √ x<br />
3 2 +a 2 )+C<br />
<strong>Exercise</strong> 6.4<br />
Evaluate the integral.<br />
∫ ∫<br />
x−5<br />
1.<br />
x 2 −1 dx<br />
2. 6x<br />
x 2 −x+2 dx<br />
∫<br />
∫<br />
x+1<br />
3.<br />
x 2 −x−6 dx 4. −x+5<br />
x 3 −x 2 −2x dx<br />
∫ x 3 ∫<br />
+x+2<br />
−3x−1<br />
5.<br />
x 2 +2x−8 dx 6. x 3 −x dx<br />
∫ ∫<br />
2x+3<br />
7.<br />
(x+2) dx<br />
8. x−1<br />
2 x 3 +4x 2 +4x dx<br />
∫<br />
∫<br />
x+4<br />
x+2<br />
9.<br />
x 3 +3x 2 +2x dx 10. x 3 +x dx<br />
∫ ∫<br />
4x−2<br />
11.<br />
x 4 −1 dx<br />
12. 3x 2 −6<br />
x 2 −x−2 dx<br />
∫<br />
∫<br />
2x+3<br />
x 2<br />
13.<br />
x 2 +2x+1 dx 14. +2x+1<br />
dx<br />
x 3 +x<br />
∫<br />
4x 2 ∫<br />
+3<br />
15.<br />
x 3 +x 2 +x dx 16. 3x 3 +1<br />
x 3 −x 2 +x−1 dx
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