integral from 2 to 3 of x^3*arctan(x-1)

Lösung

\int_{2}^{3} x^{3} \cdot arctan (x - 1) d x

- π + \frac{8}{3} + \frac{- π + 85 arctan ( 2 ) - 24}{4}

Dezimale

16.26658 \dots

Schritte zur Lösung

\int_{2}^{3} x^{3} arctan (x - 1) d x

Wende die partielle Integration an

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

\int \frac{x ^{4}}{4 ( x ^{2} - 2 x + 2 )} d x = \frac{x ^{3}}{12} + \frac{1}{4} x^{2} + \frac{1}{2} x - arctan (x - 1)

= [\frac{1}{4} x^{4} arctan (x - 1) - (\frac{x ^{3}}{12} + \frac{1}{4} x^{2} + \frac{1}{2} x - arctan (x - 1))]_{2}^{3}

Vereinfache

= [\frac{1}{4} x^{4} arctan (x - 1) - \frac{x ^{3}}{12} - \frac{1}{4} x^{2} - \frac{1}{2} x + arctan (x - 1)]_{2}^{3}

Berechne die Grenzen:

- π + \frac{8}{3} + \frac{- π + 85 arctan ( 2 ) - 24}{4}

= - π + \frac{8}{3} + \frac{- π + 85 arctan ( 2 ) - 24}{4}

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

\int_{0}^{1} c x d x

\int_{0}^{2 π} 7 t 2 d t

\int_{0}^{\infty} 13 x e^{2 x} d x

\int_{1}^{2} 5 x^{3} d x