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

Lösung

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

3 (- \frac{31}{25} + \frac{32}{5} ln (2))

Dezimale

9.58842 \dots

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende die partielle Integration an

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

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

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

Berechne die Grenzen:

- \frac{31}{25} + \frac{32}{5} ln (2)

= 3 (- \frac{31}{25} + \frac{32}{5} ln (2))

\frac{\partial}{\partial x} (\frac{y}{z})

\frac{d}{d x} (x^{3} - \frac{5}{x} + 4)

\int \frac{2}{3 3 t} - \frac{3}{1 + t ^{2}} d t

\frac{d}{d x} (200)

s l o p e x x