integral of (arctan(x)-ln(x))

Lösung

\int (arctan (x) - ln (x)) d x

x arctan (x) - \frac{1}{2} ln x^{2} + 1 - x ln (x) + x + C

Schritte zur Lösung

\int arctan (x) - ln (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int arctan (x) d x - \int ln (x) d x

\int arctan (x) d x = x arctan (x) - \frac{1}{2} ln x^{2} + 1

\int ln (x) d x = x ln (x) - x

= x arctan (x) - \frac{1}{2} ln x^{2} + 1 - (x ln (x) - x)

Vereinfache

= x arctan (x) - \frac{1}{2} ln x^{2} + 1 - x ln (x) + x

Füge eine Konstante zur Lösung hinzu

= x arctan (x) - \frac{1}{2} ln x^{2} + 1 - x ln (x) + x + C

\int (12 x + 7) d x

t a y l or (x^{2} + 25)^{- 3}

x \to - 4 - lim (\frac{- 6 x}{x + 4})

d er i v a t i v e 3 cos (5 ln (x))

\frac{\partial}{\partial y} (4 x)