integral from 1 to 3 of x^4(ln(x))^2

Lösung

\int_{1}^{3} x^{4} (ln (x))^{2} d x

\frac{484}{125} + \frac{243}{5} ln^{2} (3) - \frac{486}{25} ln (3)

Dezimale

41.17269 \dots

Schritte zur Lösung

\int_{1}^{3} x^{4} (ln (x))^{2} d x

Wende die partielle Integration an

= [\frac{1}{5} x^{5} ln^{2} (x) - \int \frac{2}{5} x^{4} ln (x) d x]_{1}^{3}

\int \frac{2}{5} x^{4} ln (x) d x = \frac{2}{5} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

= [\frac{1}{5} x^{5} ln^{2} (x) - \frac{2}{5} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})]_{1}^{3}

Berechne die Grenzen:

\frac{484}{125} + \frac{243}{5} ln^{2} (3) - \frac{486}{25} ln (3)

= \frac{484}{125} + \frac{243}{5} ln^{2} (3) - \frac{486}{25} ln (3)

d er i v a t i v e 8 e^{- 2 x}

f (x) = x - 2 sin (x)

x \to 0 lim (\frac{2}{x ^{6}})

n = 1 \sum \infty \frac{4 ^{n}}{n ^{2}}

t a y l or \frac{1}{1 + x ^{2}}