integral of arccot(5x)

Lösung

\int arccot (5 x) d x

x arccot (5 x) + \frac{1}{10} ln 25 x^{2} + 1 + C

Schritte zur Lösung

\int arccot (5 x) d x

Wende die partielle Integration an

= x arccot (5 x) - \int - \frac{5 x}{25 x ^{2} + 1} d x

\int - \frac{5 x}{25 x ^{2} + 1} d x = - \frac{1}{10} ln 25 x^{2} + 1

= x arccot (5 x) - (- \frac{1}{10} ln 25 x^{2} + 1)

Vereinfache

= x arccot (5 x) + \frac{1}{10} ln 25 x^{2} + 1

Füge eine Konstante zur Lösung hinzu

= x arccot (5 x) + \frac{1}{10} ln 25 x^{2} + 1 + C

y^{^{'}} + \frac{2}{3} y = 1 - \frac{1}{2} t

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a re a y = 9 x^{2} ln (x), y = 36 ln (x)