integral from 1/7 to 5 of 14xln(7x)

Lösung

\int_{\frac{1}{7}}^{5} 14 x ln (7 x) d x

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

Dezimale

534.75733 \dots

Schritte zur Lösung

\int_{\frac{1}{7}}^{5} 14 x ln (7 x) d x

Entferne die Konstante:

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

= 14 \cdot \int_{\frac{1}{7}}^{5} x ln (7 x) d x

Wende die partielle Integration an

= 14 [\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}

= 14 [\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)

= 14 (- \frac{306}{49} + \frac{25}{2} ln (35))

\int_{1}^{4} \frac{x ^{2} + 6}{5 x - x ^{2}} d x

\int x^{7} sin (1 + x^{\frac{9}{2}}) d x

x \to - \infty lim (2^{x} + 3)

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 5 + e^{\frac{x}{2}}

d er i v a t i v e x^{2} (1 - 8 x)