integral from 4 to 7 of xln(ln(x))

Lösung

\int_{4}^{7} x ln (ln (x)) d x

\frac{49 ln ( ln ( 7 ) ) - Ei ( 2 ln ( 7 ) ) - 16 ln ( 2 ln ( 2 ) ) + Ei ( 2 ln ( 4 ) )}{2}

Schritte zur Lösung

\int_{4}^{7} x ln (ln (x)) d x

Wende die partielle Integration an

= [\frac{1}{2} x^{2} ln (ln (x)) - \int \frac{x}{2 ln ( x )} d x]_{4}^{7}

\int \frac{x}{2 ln ( x )} d x = \frac{1}{2} Ei (2 ln (x))

= [\frac{1}{2} x^{2} ln (ln (x)) - \frac{1}{2} Ei (2 ln (x))]_{4}^{7}

Vereinfache

[\frac{1}{2} x^{2} ln (ln (x)) - \frac{1}{2} Ei (2 ln (x))]_{4}^{7} : [\frac{1}{2} (x^{2} ln (ln (x)) - Ei (2 ln (x)))]_{4}^{7}

= [\frac{1}{2} (x^{2} ln (ln (x)) - Ei (2 ln (x)))]_{4}^{7}

Berechne die Grenzen:

\frac{49 ln ( ln ( 7 ) ) - Ei ( 2 ln ( 7 ) ) - 16 ln ( 2 ln ( 2 ) ) + Ei ( 2 ln ( 4 ) )}{2}

= \frac{49 ln ( ln ( 7 ) ) - Ei ( 2 ln ( 7 ) ) - 16 ln ( 2 ln ( 2 ) ) + Ei ( 2 ln ( 4 ) )}{2}

\int_{x - 2}^{x + 2} \frac{3}{220} y d y

\int_{l n (5)}^{l n (7)} e^{- x} d x

\int_{0}^{c} x (c - x) d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} x d x

\int_{- 1}^{1} [(2 - x^{2}) - (x^{2})] d x