Integrale mit Polynomdivision mit Rest
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Exercise:
nprvmulticols prvmulticols abcliste %a abc displaystyle fracx^ - x - x - ddx %b abc displaystyle frac-x^ + x + x + ddx %c abc displaystyle frac-x^ + x - -x + ddx %d abc displaystyle fracx^ - x + x - ddx %e abc displaystyle fracx^ + x - -x - ddx %f abc displaystyle fracx^ + x + x + ddx %g abc displaystyle frac-x^ + x - -x + ddx %h abc displaystyle frac-x^ - x + x - ddx %i abc displaystyle fracx^ + x - x + ddx %j abc displaystyle frac-x^ + x + x - ddx %k abc displaystyle frac-x^ - x - -x - ddx %l abc displaystyle fracx^ - x - x - ddx abcliste multicols
Solution:
abcliste % a abc Polynomdivision dann Integration: polynomdivision polylongdivx^ - x - x - fracx^ - x - x - ddx !left x + + fracx - rightddx x^ + x + tfracln|x - | + C % b abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x + x + frac-x^ + x + x + ddx !left - x + fracx + rightddx x - tfracx^ + tfracln|x + | + C % c abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x - -x + frac-x^ + x - -x + ddx !left x - + frac-x + rightddx tfracx^ - x - tfracln|-x + | + C % d abc Polynomdivision dann Integration: polynomdivision polylongdivx^ - x + x - fracx^ - x + x - ddx !left x - + fracx - rightddx tfracx^ - x + tfracln|x - | + C % e abc Polynomdivision dann Integration: polynomdivision polylongdivx^ + x - -x - fracx^ + x - -x - ddx !left - x + frac-x - rightddx x - x^ - tfracln|-x - | + C % f abc Polynomdivision dann Integration: polynomdivision polylongdivx^ + x + x + fracx^ + x + x + ddx !left x + - fracx + rightddx tfracx^ + x - tfracln|x + | + C % g abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x - -x + frac-x^ + x - -x + ddx !left x - - frac-x + rightddx x^ - x + tfracln|-x + | + C % h abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ - x + x - frac-x^ - x + x - ddx !left -x - + fracx - rightddx -tfracx^ - x + tfracln|x - | + C % i abc Polynomdivision dann Integration: polynomdivision polylongdivx^ + x - x + fracx^ + x - x + ddx !left x - - fracx + rightddx x^ - x - ln|x + | + C % j abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x + x - frac-x^ + x + x - ddx !left - x + fracx - rightddx x - tfracx^ + tfracln|x - | + C % k abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ - x - -x - frac-x^ - x - -x - ddx !left x + - frac-x - rightddx tfracx^ + x + tfracln|-x - | + C % l abc Polynomdivision dann Integration: polynomdivision polylongdivx^ - x - x - fracx^ - x - x - ddx !left x + + fracx - rightddx tfracx^ + x + tfracln|x - | + C abcliste
nprvmulticols prvmulticols abcliste %a abc displaystyle fracx^ - x - x - ddx %b abc displaystyle frac-x^ + x + x + ddx %c abc displaystyle frac-x^ + x - -x + ddx %d abc displaystyle fracx^ - x + x - ddx %e abc displaystyle fracx^ + x - -x - ddx %f abc displaystyle fracx^ + x + x + ddx %g abc displaystyle frac-x^ + x - -x + ddx %h abc displaystyle frac-x^ - x + x - ddx %i abc displaystyle fracx^ + x - x + ddx %j abc displaystyle frac-x^ + x + x - ddx %k abc displaystyle frac-x^ - x - -x - ddx %l abc displaystyle fracx^ - x - x - ddx abcliste multicols
Solution:
abcliste % a abc Polynomdivision dann Integration: polynomdivision polylongdivx^ - x - x - fracx^ - x - x - ddx !left x + + fracx - rightddx x^ + x + tfracln|x - | + C % b abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x + x + frac-x^ + x + x + ddx !left - x + fracx + rightddx x - tfracx^ + tfracln|x + | + C % c abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x - -x + frac-x^ + x - -x + ddx !left x - + frac-x + rightddx tfracx^ - x - tfracln|-x + | + C % d abc Polynomdivision dann Integration: polynomdivision polylongdivx^ - x + x - fracx^ - x + x - ddx !left x - + fracx - rightddx tfracx^ - x + tfracln|x - | + C % e abc Polynomdivision dann Integration: polynomdivision polylongdivx^ + x - -x - fracx^ + x - -x - ddx !left - x + frac-x - rightddx x - x^ - tfracln|-x - | + C % f abc Polynomdivision dann Integration: polynomdivision polylongdivx^ + x + x + fracx^ + x + x + ddx !left x + - fracx + rightddx tfracx^ + x - tfracln|x + | + C % g abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x - -x + frac-x^ + x - -x + ddx !left x - - frac-x + rightddx x^ - x + tfracln|-x + | + C % h abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ - x + x - frac-x^ - x + x - ddx !left -x - + fracx - rightddx -tfracx^ - x + tfracln|x - | + C % i abc Polynomdivision dann Integration: polynomdivision polylongdivx^ + x - x + fracx^ + x - x + ddx !left x - - fracx + rightddx x^ - x - ln|x + | + C % j abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ + x + x - frac-x^ + x + x - ddx !left - x + fracx - rightddx x - tfracx^ + tfracln|x - | + C % k abc Polynomdivision dann Integration: polynomdivision polylongdiv-x^ - x - -x - frac-x^ - x - -x - ddx !left x + - frac-x - rightddx tfracx^ + x + tfracln|-x - | + C % l abc Polynomdivision dann Integration: polynomdivision polylongdivx^ - x - x - fracx^ - x - x - ddx !left x + + fracx - rightddx tfracx^ + x + tfracln|x - | + C abcliste