integral from 0 to 1 of xarctan(x^2)

Lösung

\int_{0}^{1} x arctan (x^{2}) d x

\frac{π}{8} - \frac{1}{4} ln (2)

Dezimale

0.21941 \dots

Schritte zur Lösung

\int_{0}^{1} x arctan (x^{2}) d x

Wende die partielle Integration an

= [\frac{1}{2} x^{2} arctan (x^{2}) - \int \frac{x ^{3}}{x ^{4} + 1} d x]_{0}^{1}

\int \frac{x ^{3}}{x ^{4} + 1} d x = \frac{1}{4} ln x^{4} + 1

= [\frac{1}{2} x^{2} arctan (x^{2}) - \frac{1}{4} ln x^{4} + 1]_{0}^{1}

Berechne die Grenzen:

\frac{π}{8} - \frac{1}{4} ln (2)

= \frac{π}{8} - \frac{1}{4} ln (2)

\int_{0}^{1} - x^{2} + 2 x d x

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\int_{0}^{1} sin (x^{3}) d x

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