integral from 1 to 25 of sqrt(x)ln(x)

Lösung

\int_{1}^{25} x ln (x) d x

- \frac{496}{9} + \frac{500}{3} ln (5)

Dezimale

213.12854 \dots

Schritte zur Lösung

\int_{1}^{25} x ln (x) d x

Wende die partielle Integration an

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

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}]_{1}^{25}

Berechne die Grenzen:

- \frac{496}{9} + \frac{500}{3} ln (5)

= - \frac{496}{9} + \frac{500}{3} ln (5)

d er i v a t i v e f (x) = \frac{x}{x}

y^{^{'''}} - 4 y^{^{''}} + 4 y^{^{'}} = 8 x

\frac{d}{d x} (sin (5 π x))

\frac{d}{d x} (12 ln (\frac{x}{20}))

\int 1 - x^{3} d x