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

Lösung

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

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

Dezimale

1048.12438 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= 14 [\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x]_{\frac{1}{5}}^{7}

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

= 14 [\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}]_{\frac{1}{5}}^{7}

Berechne die Grenzen:

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

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

\int 4 sin (2 x) - 3 cos (6 x) d x

\int_{0}^{\frac{π}{3}} 49 sin^{2} (x) d x

\int \frac{x ^{3} - 1}{( 2 x ^{4} - 8 x ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (2 cos (x) + cos^{2} (x))

\frac{\partial}{\partial x} (\frac{c ^{2} - x ^{2}}{2 x})