integral from 1/7 to 3 of 12xln(7x)

Lösung

\int_{\frac{1}{7}}^{3} 12 x ln (7 x) d x

12 (- \frac{110}{49} + \frac{9}{2} ln (21))

Dezimale

137.46543 \dots

Schritte zur Lösung

\int_{\frac{1}{7}}^{3} 12 x ln (7 x) d x

Entferne die Konstante:

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

= 12 \cdot \int_{\frac{1}{7}}^{3} x ln (7 x) d x

Wende die partielle Integration an

= 12 [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{3}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 12 [\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}]_{\frac{1}{7}}^{3}

Berechne die Grenzen:

- \frac{110}{49} + \frac{9}{2} ln (21)

= 12 (- \frac{110}{49} + \frac{9}{2} ln (21))

\frac{d}{d x} (\frac{sin ( x )}{x ^{3}})

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 10 y^{2}))

f (x) = x - cos (x)

\int_{0}^{6} 2. 3^{t} sin (\frac{t}{2}) d t

\int \frac{( 2 x + 4 )}{x ^{2} + 4 x + 5} d x