FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.73(B) (^) a x 2 dx 1 a x− 2 =2a a xlog +− ,(x a)<
(c) 2 2 (^22 )
dx log x x a
x a
= + ±
(^) ±
Example 152: (^) x 13dx (^2) −
2
I^3 dx^3 dx
= (^) x 1− = (^) (x 1)(x 1)+ −
3 1 1 dx
2 x 1 x 1
=^ −^
(^) − +
3 1 dx dx
2 x 1 x 1
=^ −^
−^ +
=^32 {log(x 1) log(x 1)− − + }
=3 x 12 x 1log −+
Example 153: (^) x 1xdx (^4) − Let x^2 = u, then 2xdx = du
2
2 2
I 1 du 1 1 u 1 1 x 1. log log
2 u 1 2 2 u 1 4 x 1
∴ = = − = −
(^) − + +
Example 154: (^) 4 xdx− 2
I dx 1 1 1 dx 1 dx 1 dx
(2 x)(2 x) 4 2 x 2 x 4 2 x 4 2 x
= =^ +^ = +
(^) + − (^) + − + (^) −
(^1) log(2 x) log(2 x) log 1 1 2 x
4 4 4 2 x
= + − − = +
−
Alternative way. (^) 2 x 2 dx 1 2 x− 2 =4 2 xlog +−
Example 155: (^) 2x 3x 2 (^4) −x (^2) − dx Let x^2 = u, 2xdx = du
2
I^1 du^1 du
= 2 2u 3u 2− − =2 (u 2)(2u 1) (^) − +