integral from 2 to 5 of x^2ln(3x)

Lösung

\int_{2}^{5} x^{2} ln (3 x) d x

- 13 + \frac{ln ( \frac{5 ^{125} \cdot 3 ^{117}}{256} )}{3}

Dezimale

95.05739 \dots

Schritte zur Lösung

\int_{2}^{5} x^{2} ln (3 x) d x

Wende die partielle Integration an

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

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

= [\frac{1}{3} x^{3} ln (3 x) - \frac{x ^{3}}{9}]_{2}^{5}

Berechne die Grenzen:

- 13 + \frac{- 8 ln ( 6 ) + 125 ln ( 15 )}{3}

= - 13 + \frac{- 8 ln ( 6 ) + 125 ln ( 15 )}{3}

Vereinfache

= - 13 + \frac{ln ( \frac{5 ^{125} \cdot 3 ^{117}}{256} )}{3}

x \frac{d y}{d x} + y = sec (x y)

\frac{d}{d x} (2 x e^{x + 3} + e^{x + 3} x^{2})

s l o p e e ln (2 x^{4} + a x^{2} y^{2 + 2 y^{4}})

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

n = 0 \sum \infty (\frac{- 1}{3})^{2 n}