\(\int \frac {x}{1+x^4} dx =\)
\(\int \frac{x^3}{1+x^4} dx =\)
\(\int \frac{4x^2 +5}{x^3 -2x^2 +x} dx =\)
\(\int \frac{2x}{x^2 -6x +5} dx =\)
\(\int \frac{dx}{x^2 (x-1)} =\)
\(\int \frac{3x +4}{x^2 +2x +2} dx = \)
\(\int \frac{2x^3 -11x^2 +4x -4}{x^4 -2x^3} dx =\)
\(\int \frac{2x + 1}{x^2 -6x +12} dx =\)
Výsledky:
\(\frac{1}{2} \arctan x^2 +C\)
\(\frac{1}{4} \ln (1+x^4) +C\)
\(5 \ln |x| - ln |x-1| - \frac{9}{x-1} +C\)
\(\frac{5}{2} \ln |x-5| - \frac{1}{2} \ln |x-1| + C\)
\(\ln |x-1| - \ln |x| + \frac{1}{x} + C\)
\(\frac{3}{2} \ln |x^2 +2x +2| + \arctan (x+1) + C\)
\(5 \ln |x| -3 \ln |x-2| + \frac{1}{x} - \frac{1}{x^2} + C\)
\(\ln |x^2 -6x +12| + \sqrt {3} \arctan \frac{2x -1}{\sqrt {3}} +C\)