FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.77
(^1) u 4 du (^221) u 4 du 2 2
= 5 + = 5 +
( )
1 u u 4 4^22222
5 2 2 log u u 4
(^) + (^)
= + + +
(by formula 1)
( )
1 5x 25x 16 16^22
5 2 2 log 5x 25x 16
(^) +
= + + +
(^)
( )
x 25x 16 8^22
= 2 + + 5 log 5x 25x 16 c.+ + +
SELF EXAMINATION QUESTIONS
Integrate :
- x^2 ex. [Ans. x^2 ex + 2ex – 2xex, c is added in every case]
- xe4x [Ans. ( )
e4x
16 4x 1− +c^ ] - xeax. [Ans. ( )
ax
2
e ax 1
a − +c]
- x log x [Ans.
x^2 x^2
2 logx− 4 +c] - x^3 ex. [Ans. x^3 ex – 3x^2 ex + 6xex – 6xx]
- (log x)^2. [Ans. x (log x)^2 – 2x log x + 2x+c]
- x (log x)^2. [Ans. ( )
x^22 x^2 x^2
2 logx − 2 logx+ 4 +c] - (i) logxx 2
Ans. logx 1 c
x x
(^) − − +
(^)
(ii) 2
log(1 x)dx
(1 x)
+
+
Ans. logx 1 c
x x
(^) − − +
(^)
- (x + 1)^2 log x
1 3 1 x 3 2 1
Ans. logx(x 1) x 3 + −9 2 3− − −x logx c+^
10.^12 log(logx). [Ans. log x {log(logx)–1}+c]