Lab sheet 7

Exercise 1
--> y : integrate ( ( ( x ^ 3 + 1 ) / ( x ^ 2 + 1 ) ) ^ 3 , x ) $
--> wxplot2d ( [ y , x ^ 4 / 4 ] , [ x , 1 , 10 ] , [ legend , "y" , "x^4/4" ] ) ;

\[\operatorname{ }\]

 (Graphics)

\[\operatorname{ }\]

--> kill ( y ) $
Exercise 2
--> assume ( c > 0 ) $ assume ( d > 0 ) $
--> y : integrate ( ( a · x ^ 2 + b ) / ( c · x ^ 2 + d ) , x ) ;

\[\operatorname{(y) }\frac{a x}{c}-\frac{\left( 2 a d-2 b c\right) \operatorname{atan}\left( \frac{\sqrt{c} x}{\sqrt{d}}\right) }{2 {{c}^{\frac{3}{2}}} \sqrt{d}}\]

--> limit ( y / x , x , inf ) ;

\[\operatorname{ }\frac{a}{c}\]

Exercise 3
--> integrate ( x / ( x ^ 2 + 1 ) , x ) ;

\[\operatorname{ }\frac{\log{\left( {{x}^{2}}+1\right) }}{2}\]

Exercise 4
--> b : random ( 11 ) 5 $ c : random ( 11 ) 5 $
y : x ^ 2 + b · x + c ; Δ : b ^ 2 4 · c ; I : integrate ( 1 / y , x ) ;
wxplot2d ( y , [ x , 10 , 10 ] , [ box , false ] , [ axes , solid ] ) ;

\[\operatorname{(y) }{{x}^{2}}+2 x+3\]

\[\operatorname{(\Delta ) }-8\]

\[\operatorname{(I) }\frac{\operatorname{atan}\left( \frac{2 x+2}{{{2}^{\frac{3}{2}}}}\right) }{\sqrt{2}}\]

\[\operatorname{ }\]

 (Graphics)

\[\operatorname{ }\]

Exercise 5: omitted
Exercise 6: omitted

Created with wxMaxima.

The source of this Maxima session can be downloaded here.