integral from 1/7 to 5 of 6xln(7x)

Lösung

\int_{\frac{1}{7}}^{5} 6 x ln (7 x) d x

6 (- \frac{306}{49} + \frac{25}{2} ln (35))

Dezimale

229.18171 \dots

Schritte zur Lösung

\int_{\frac{1}{7}}^{5} 6 x ln (7 x) d x

Entferne die Konstante:

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

= 6 \cdot \int_{\frac{1}{7}}^{5} x ln (7 x) d x

Wende die partielle Integration an

= 6 [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{5}

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

= 6 [\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}]_{\frac{1}{7}}^{5}

Berechne die Grenzen:

- \frac{306}{49} + \frac{25}{2} ln (35)

= 6 (- \frac{306}{49} + \frac{25}{2} ln (35))

x \to \frac{π}{2} lim (x \cdot sec (x))

\frac{d}{d x} (- \frac{2 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}})

x \to \frac{π}{2} lim (cot (x))

n = 5 \sum \infty \frac{1}{2 ^{n}}

\frac{d}{d x} (7 x^{2} ln (x))