integral from 0 to x of arctan(x)

Lösung

\int_{0}^{x} arctan (x) d x

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

Schritte zur Lösung

\int_{0}^{x} arctan (x) d x

Wende die partielle Integration an

= [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{x}

\int \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln x^{2} + 1

= [x arctan (x) - \frac{1}{2} ln x^{2} + 1]_{0}^{x}

Berechne die Grenzen:

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

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

\int_{0}^{5} (25 - x^{2}) d x

\int_{2}^{6} \frac{x}{x ^{2} - 3} d x

\int_{0}^{3} \frac{1}{x ^{2} + 1} d x

\int_{e^{- 1}}^{e^{1}} ∣ ln (x) ∣ d x

\int_{1}^{3} (1 + ln (x)) x^{x} d x