diff --git a/changelog b/changelog index eda7bfd..456e2f9 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20080417 tpd src/input/schaum7.input fix typo in --S 30 +20080417 tpd src/input/schaum5.input fix typo 14:88 -> 14:123 20080416 tpd src/input/schaum7.input show Schaums-Axiom equivalence 20080416 tpd src/input/schaum6.input show Schaums-Axiom equivalence 20080416 tpd src/input/schaum5.input show Schaums-Axiom equivalence diff --git a/src/input/schaum5.input.pamphlet b/src/input/schaum5.input.pamphlet index 50ea618..a5d3fc3 100644 --- a/src/input/schaum5.input.pamphlet +++ b/src/input/schaum5.input.pamphlet @@ -1571,7 +1571,7 @@ cc3:=aa2-bb1 --R Type: Expression Integer --E ---S 42 14:88 Axiom cannot simplify these results +--S 42 14:123 Axiom cannot simplify these results cc4:=aa2-bb2 --R --R (14) diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet index 3062d2e..ce37f19 100644 --- a/src/input/schaum7.input.pamphlet +++ b/src/input/schaum7.input.pamphlet @@ -356,71 +356,64 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x) --E --S 30 -bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2)) +bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2)) --R ---R 2 ---R x 2 ---R - 2x log(-------) + a ---R 2 2 ---R x - a ---R (2) ---------------------- ---R 4 ---R 4a x +--R 2 +--R 2 x 2 +--R - x log(-------) + a +--R 2 2 +--R x - a +--R (2) --------------------- +--R 4 2 +--R 2a x --R Type: Expression Integer --E --S 31 -cc:=aa-bb ---R ---R 2 ---R 2 2 2 2 2 x 2 2 ---R 2x log(x - a ) - 4x log(x) + 2x log(-------) - a x + 2a ---R 2 2 ---R x - a ---R (3) --------------------------------------------------------- ---R 4 2 ---R 4a x ---R Type: Expression Integer ---E - ---S 32 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a ---R (4) log(-) == - log(b) + log(a) +--R (3) log(-) == - log(b) + log(a) --R b --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 33 -dd:=divlog cc +--S 32 +t1:=divlog bb --R ---R 2 2 2 2 2 ---R 2x log(x ) - 4x log(x) - a x + 2a ---R (5) ---------------------------------- ---R 4 2 ---R 4a x +--R 2 2 2 2 2 2 +--R - x log(x ) + x log(x - a ) + a +--R (4) --------------------------------- +--R 4 2 +--R 2a x --R Type: Expression Integer --E ---S 34 +--S 33 logpow:=rule(log(a^n) == n*log(a)) --R --R n ---R (6) log(a ) == n log(a) +--R (5) log(a ) == n log(a) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 35 14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT -ee:=logpow dd +--S 34 +t2:=logpow t1 --R ---R - x + 2 ---R (7) ------- ---R 2 2 ---R 4a x +--R 2 2 2 2 2 +--R x log(x - a ) - 2x log(x) + a +--R (6) ------------------------------- +--R 4 2 +--R 2a x --R Type: Expression Integer --E +--S 35 14:150 Schaums and Axiom agree +cc:=aa-t2 + + (7) 0 + Type: Expression Integer +--E @ \section{\cite{1}:14.151~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^2}}$}