082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

13.2 Elementary integration 441
2 (a)
e 5x
5 +c (b) e 6x
6 +c
(c) − e−3t
3 +c (d) −e−x +c
(e) 2e 0.5t +c (f) 3e z/3 +c
(g) − e−4t
4
3 (a) − cos4x +c
4
(b) − cos9t +c
9 ( )
x
(c) −2cos +c
2
(d) − 5 2 cos (
(e)
sin7x
7
+c (h) −2e−2.5x
5
+c
2t
5
)
+c
(f) − 1 sin(−3x) +c
3 ( )
3
(g)
5 sin 5t
+c
3
ln|sec9x|
(h) +c
9
1
(i) (ln|cosec2x −cot2x|) +c
2
1
(j) (ln|sec5t +tan5t|)+c
5
1
(k)
8 ln|sin8y|+c
1
(l) sin(5t +1) +c
5
(m) 1 ln|sec(3x +4)| +c
3
(n) − 1 cos(3t −π)+c
3
1
5
+c
(o) ln|cosec(5z +2) −cot(5z +2)| +c
( ) ( )∣ (p) 2ln
∣ sec x
2 +1 x ∣∣∣∣
+tan
2 +1 +c
( )
(q) − 3 2 cos 2t
3 −1 +c
(r) −ln|sin(5 −x)| +c
(s) − 1 ln|cosec(π −2x) −cot(π −2x)| +c
2
4 (a) tan −1 x +c
(b) sin −1 x +c
( )
(c) sin −1 x
+c
2
(d)
( )
1 z
3 tan−1 +c
3
(e) sin −1 (2x) +c
(f) 10tan −1 (10v) +c
( )
(g) 10 −3 tan −1 x
10 3 +c
(h)
( )
1
√ tan −1 t
√ +c
10 10
( )
(i) sin −1 x
√ +c
2
(j) 3tan −1 (3x) +c
5 (a) 3x+ x2
2 +ln|x|+c
(b) e2x
2 + e−2x +c
2
(c) − 2 sin3x
cos(3x) + +c
3 3
(d) 0.5ln|sec(2t + π) +tan(2t + π)|
( )∣ +2ln
∣ sin t ∣∣∣∣
2 − π +c
( )∣ (e) 2ln
∣ sec t ∣∣∣∣
+ 1 ln|cosec(3t − π)
2 3
−cot(3t −π)|+c
(f) −cosx+ x2
6 −e−x +c
(g) 1 3 ln|sec3x+tan3x|+c
(h) t3 3 +2t−1 t +c
(i) − e−2x +c
6
1
(j) ln|sec(4t −3)| +2cos(−t −1) +c
4
(k)x+ 2 3 ln|sin3x|+c
( ) ( )
t t
(l) −2cos −6sin +c
2 2
(m) t3 3 −2t2 +4t+c
(n) −3e −t +2e −t/2 +c
(o)7x−x 7 −e −x +c
(p) k 2 t +kt 2 + t3 3 +c
(q) −kcost − sinkt
k
+c