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https://texercises.com/exercise/integrale-rationaler-funktionen-mit-linearem-zahler-und-quadratischem-nenner/
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Exercise:
prvmulticols nprvmulticols abclist %a abc displaystyle fracx + x^ + x + ddx %b abc displaystyle fracx - x^ - x + ddx %c abc displaystyle frac-x + x^ + x + ddx %d abc displaystyle fracx + x^ - x + ddx %e abc displaystyle frac-x - x^ + x + ddx %f abc displaystyle fracx + x^ + x + ddx %g abc displaystyle fracx + x^ + ddx %h abc displaystyle frac-x + x^ - x + ddx %i abc displaystyle fracx - x^ + x + ddx %j abc displaystyle fracx + x^ - x + ddx %k abc displaystyle fracx - x^ + x + ddx %l abc displaystyle frac-x + x^ + x + ddx %m abc displaystyle fracx - x^ - x + ddx %n abc displaystyle fracx + x^ + ddx %o abc displaystyle frac-x + x^ - x + ddx %p abc displaystyle fracx + x^ + ddx %q abc displaystyle frac-x - x^ - x + ddx %r abc displaystyle fracx + x^ + x + ddx %s abc displaystyle frac-x + x^ - x + ddx %t abc displaystyle fracx - x^ + x + ddx %u abc displaystyle fracx + x^ - x + ddx abclist multicols

Solution:
abclist %a abc fracx + x^ + x + ddx fracx+ + x^+x+ddx fracx+x^+x+ddx + fracx^+x+ddx lnx^+x+ + tfracsqrt arctan!fracx+sqrt + C %b abc fracx - x^ - x + ddx fractfracx- + tfracx^ - x + ddx tfrac fracx-x^ - x + ddx + tfrac fracx^ - x + ddx tfrac lnx^ - x + + tfracsqrt arctan!fracx-sqrt + C %c abc frac-x + x^ + x + ddx frac-tfracx+ + x^+x+ddx -tfrac fracx+x^+x+ddx + fracx^+x+ddx -tfrac lnx^+x+ + tfrac arctan!fracx+ + C %d abc fracx + x^ - x + ddx fracx- + x^ - x + ddx fracx-x^ - x + ddx + fracx^ - x + ddx ln|x^-x+| + tfracsqrt ln!Bigg|fracx--sqrtx-+sqrtBigg| + C %e abc frac-x - x^ + x + ddx frac-x+ + x^+x+ddx - fracx+x^+x+ddx + fracx^+x+ddx -lnx^+x+ + tfracsqrt arctan!fracx+sqrt + C %f abc fracx + x^ + x + ddx fractfracx+ + x^+x+ddx tfrac fracx+x^+x+ddx + fracx^+x+ddx tfrac lnx^+x+ + arctanx+ + C %g abc fracx + x^ + ddx fractfracx + x^+ddx tfrac fracxx^+ddx + fracx^+ddx tfrac lnx^+ + arctanx + C %h abc frac-x + x^ - x + ddx frac-tfracx- + x^-x+ddx -tfrac fracx-x^-x+ddx + fracx^-x+ddx -tfraclnx^-x+ + arctanx- + C %i abc fracx - x^ + x + ddx fracx+ - x^+x+ddx fracx+x^+x+ddx - fracx^+x+ddx lnx^+x+ - tfracsqrt arctan!fracx+sqrt + C %j abc fracx + x^ - x + ddx fracx- + x^-x+ddx fracx-x^-x+ddx + fracx^-x+ddx lnx^-x+ + arctanx- + C %k abc fracx - x^ + x + ddx fractfracx+ - tfracx^+x+ddx tfrac fracx+x^+x+ddx - tfrac fracx^+x+ddx tfraclnx^+x+ - tfracsqrtarctan!fracx+sqrt + C %l abc frac-x + x^ + x + ddx frac-tfracx+ + tfracx^+x+ddx -tfrac fracx+x^+x+ddx + tfrac fracx^+x+ddx -tfraclnx^+x+ + tfracsqrtarctan!fracx+sqrt + C %m abc fracx - x^ - x + ddx fractfracx- - tfracx^-x+ddx tfrac fracx-x^-x+ddx - tfrac fracx^-x+ddx tfraclnx^-x+ - tfracsqrt arctan!fracx-sqrt + C %n abc fracx + x^ + ddx fractfracx + x^+ddx tfrac fracxx^+ddx + fracx^+ddx tfraclnx^+ + tfracarctan!fracx + C %o abc frac-x + x^ - x + ddx frac-x- + x^-x+ddx - fracx-x^-x+ddx + fracx^-x+ddx -lnx^-x+ + tfracsqrt arctan!fracx-sqrt + C %p abc fracx + x^ + ddx fracxx^+ddx + fracx^+ddx lnx^+ + tfracsqrtarctan!fracxsqrt + C %q abc frac-x - x^ - x + ddx frac-tfracx- - tfracx^-x+ddx -tfrac fracx-x^-x+ddx - tfrac fracx^-x+ddx -tfraclnx^-x+ - tfracsqrt arctan!fracx-sqrt + C %r abc fracx + x^ + x + ddx fractfracx+ + tfracx^+x+ddx tfrac fracx+x^+x+ddx + tfrac fracx^+x+ddx tfraclnx^+x+ + tfracsqrt arctan!fracx+sqrt + C %s abc frac-x + x^ - x + ddx frac-x- + x^-x+ddx - fracx-x^-x+ddx + fracx^-x+ddx -lnx^-x+ + tfracsqrt arctan!fracx-sqrt + C %t abc fracx - x^ + x + ddx fracx+ - x^+x+ddx fracx+x^+x+ddx - fracx^+x+ddx lnx^+x+ - arctan!fracx+sqrt + C %u abc fracx + x^ - x + ddx fracx- + x^-x+ddx fracx-x^-x+ddx + fracx^-x+ddx lnx^-x+ + tfracsqrt arctan!fracx-sqrt + C abclist
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Exercise:
prvmulticols nprvmulticols abclist %a abc displaystyle fracx + x^ + x + ddx %b abc displaystyle fracx - x^ - x + ddx %c abc displaystyle frac-x + x^ + x + ddx %d abc displaystyle fracx + x^ - x + ddx %e abc displaystyle frac-x - x^ + x + ddx %f abc displaystyle fracx + x^ + x + ddx %g abc displaystyle fracx + x^ + ddx %h abc displaystyle frac-x + x^ - x + ddx %i abc displaystyle fracx - x^ + x + ddx %j abc displaystyle fracx + x^ - x + ddx %k abc displaystyle fracx - x^ + x + ddx %l abc displaystyle frac-x + x^ + x + ddx %m abc displaystyle fracx - x^ - x + ddx %n abc displaystyle fracx + x^ + ddx %o abc displaystyle frac-x + x^ - x + ddx %p abc displaystyle fracx + x^ + ddx %q abc displaystyle frac-x - x^ - x + ddx %r abc displaystyle fracx + x^ + x + ddx %s abc displaystyle frac-x + x^ - x + ddx %t abc displaystyle fracx - x^ + x + ddx %u abc displaystyle fracx + x^ - x + ddx abclist multicols

Solution:
abclist %a abc fracx + x^ + x + ddx fracx+ + x^+x+ddx fracx+x^+x+ddx + fracx^+x+ddx lnx^+x+ + tfracsqrt arctan!fracx+sqrt + C %b abc fracx - x^ - x + ddx fractfracx- + tfracx^ - x + ddx tfrac fracx-x^ - x + ddx + tfrac fracx^ - x + ddx tfrac lnx^ - x + + tfracsqrt arctan!fracx-sqrt + C %c abc frac-x + x^ + x + ddx frac-tfracx+ + x^+x+ddx -tfrac fracx+x^+x+ddx + fracx^+x+ddx -tfrac lnx^+x+ + tfrac arctan!fracx+ + C %d abc fracx + x^ - x + ddx fracx- + x^ - x + ddx fracx-x^ - x + ddx + fracx^ - x + ddx ln|x^-x+| + tfracsqrt ln!Bigg|fracx--sqrtx-+sqrtBigg| + C %e abc frac-x - x^ + x + ddx frac-x+ + x^+x+ddx - fracx+x^+x+ddx + fracx^+x+ddx -lnx^+x+ + tfracsqrt arctan!fracx+sqrt + C %f abc fracx + x^ + x + ddx fractfracx+ + x^+x+ddx tfrac fracx+x^+x+ddx + fracx^+x+ddx tfrac lnx^+x+ + arctanx+ + C %g abc fracx + x^ + ddx fractfracx + x^+ddx tfrac fracxx^+ddx + fracx^+ddx tfrac lnx^+ + arctanx + C %h abc frac-x + x^ - x + ddx frac-tfracx- + x^-x+ddx -tfrac fracx-x^-x+ddx + fracx^-x+ddx -tfraclnx^-x+ + arctanx- + C %i abc fracx - x^ + x + ddx fracx+ - x^+x+ddx fracx+x^+x+ddx - fracx^+x+ddx lnx^+x+ - tfracsqrt arctan!fracx+sqrt + C %j abc fracx + x^ - x + ddx fracx- + x^-x+ddx fracx-x^-x+ddx + fracx^-x+ddx lnx^-x+ + arctanx- + C %k abc fracx - x^ + x + ddx fractfracx+ - tfracx^+x+ddx tfrac fracx+x^+x+ddx - tfrac fracx^+x+ddx tfraclnx^+x+ - tfracsqrtarctan!fracx+sqrt + C %l abc frac-x + x^ + x + ddx frac-tfracx+ + tfracx^+x+ddx -tfrac fracx+x^+x+ddx + tfrac fracx^+x+ddx -tfraclnx^+x+ + tfracsqrtarctan!fracx+sqrt + C %m abc fracx - x^ - x + ddx fractfracx- - tfracx^-x+ddx tfrac fracx-x^-x+ddx - tfrac fracx^-x+ddx tfraclnx^-x+ - tfracsqrt arctan!fracx-sqrt + C %n abc fracx + x^ + ddx fractfracx + x^+ddx tfrac fracxx^+ddx + fracx^+ddx tfraclnx^+ + tfracarctan!fracx + C %o abc frac-x + x^ - x + ddx frac-x- + x^-x+ddx - fracx-x^-x+ddx + fracx^-x+ddx -lnx^-x+ + tfracsqrt arctan!fracx-sqrt + C %p abc fracx + x^ + ddx fracxx^+ddx + fracx^+ddx lnx^+ + tfracsqrtarctan!fracxsqrt + C %q abc frac-x - x^ - x + ddx frac-tfracx- - tfracx^-x+ddx -tfrac fracx-x^-x+ddx - tfrac fracx^-x+ddx -tfraclnx^-x+ - tfracsqrt arctan!fracx-sqrt + C %r abc fracx + x^ + x + ddx fractfracx+ + tfracx^+x+ddx tfrac fracx+x^+x+ddx + tfrac fracx^+x+ddx tfraclnx^+x+ + tfracsqrt arctan!fracx+sqrt + C %s abc frac-x + x^ - x + ddx frac-x- + x^-x+ddx - fracx-x^-x+ddx + fracx^-x+ddx -lnx^-x+ + tfracsqrt arctan!fracx-sqrt + C %t abc fracx - x^ + x + ddx fracx+ - x^+x+ddx fracx+x^+x+ddx - fracx^+x+ddx lnx^+x+ - arctan!fracx+sqrt + C %u abc fracx + x^ - x + ddx fracx- + x^-x+ddx fracx-x^-x+ddx + fracx^-x+ddx lnx^-x+ + tfracsqrt arctan!fracx-sqrt + C abclist
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Attributes & Decorations
Tags
gebrochen rationale funktion, integralrechnung, mathematik
Content image
Difficulty
(3, default)
Points
3 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration