Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.67

Example 137:

x x

x x

e e dx

e e

−

−

−

(^) + Let e
x +e–x = u, (ex –e–x)dx = du
I du logu log(e e ) cx x
u
= = = + − +
Example 138: 2 x1/x
1 e dx^1
x
(^) − (^) +
Let x +

1

x= u,^2

1 dx du^1

x

(^) − (^) =
(^)
I e du e e c= u = u= x 1/x+ +
Example 139: e e 1dxx x+
Let ex + 1 = u^2 , exdx = 2udu
I 2 u du u (e 1) c.^2 2 2^3 x 3/2
= =3 3= + +
Example 140: 2
dx
(^) x(logx) Let log x = z,
dx dz
x =
Now I = dz 2 z 1 1= −z logx= − +c.
Example 141: (^4) 2x 3x 7++ dx
I^2 (2x 3 1) dx 2 2x 3dx dx
2x 3 2x 3 2x 3

= + + = + +

(^) + (^) + (^) +
1 2
2 dx dx I I
= + (^) 2x 3+ = + where I 1 = 2 dx = 2x
and I 2 =^1 2 u 2 du 1= logu. Let 2x + 3 = u, 2dx = du
(^1) log(2x 3)
= 2 +
I 2x log(2x 3) c.^1
= + 2 + +