integral from 0 to 2 of arctan(x)

Lösung

\int_{0}^{2} arctan (x) d x

2 arctan (2) - \frac{1}{2} ln (5)

Dezimale

1.40957 \dots

Schritte zur Lösung

\int_{0}^{2} arctan (x) d x

Wende die partielle Integration an

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

\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}^{2}

Berechne die Grenzen:

2 arctan (2) - \frac{1}{2} ln (5)

= 2 arctan (2) - \frac{1}{2} ln (5)

\int_{- 1}^{- 1} 2 x d x

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\int_{1}^{5} \frac{1}{x - 0} d x

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