integral from 1/7 to 5 of 8xln(7x)

Lösung

\int_{\frac{1}{7}}^{5} 8 x ln (7 x) d x

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

Dezimale

305.57562 \dots

Schritte zur Lösung

\int_{\frac{1}{7}}^{5} 8 x ln (7 x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{\frac{1}{7}}^{5} x ln (7 x) d x

Wende die partielle Integration an

= 8 [\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}

= 8 [\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)

= 8 (- \frac{306}{49} + \frac{25}{2} ln (35))

f^{^{'}} (x) = x (x - 3)

roo t s 3 x y^{2}

\frac{\partial}{\partial z} (ln (x^{2} + y^{2} + z^{2}))

\frac{\partial}{\partial y} (e^{y} cos (x))

x \to 0 lim (e^{x + 1})