integral from 1 to 2 of (-7ln(x))/(x^2)

Lösung

\int_{1}^{2} \frac{- 7 ln ( x )}{x ^{2}} d x

- 7 (\frac{- ln ( 2 ) - 1}{2} + 1)

Dezimale

- 1.07398 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{- 7 ln ( x )}{x ^{2}} d x

Entferne die Konstante:

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

= - 7 \cdot \int_{1}^{2} \frac{ln ( x )}{x ^{2}} d x

Wende die partielle Integration an

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

\int - \frac{1}{x ^{2}} d x = \frac{1}{x}

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

Da die Nenner gleich sind, fasse die Brüche zusammen.:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

Berechne die Grenzen:

\frac{- ln ( 2 ) - 1}{2} + 1

= - 7 (\frac{- ln ( 2 ) - 1}{2} + 1)

\int \frac{- 7}{cos ( x ) - 1} d x

\int tan^{3} (2 x) sec^{4} (2 x) d x

\int_{x}^{x + 2} (4 t + 1) d t

\frac{\partial}{\partial x} (2 cos (x y))

n or ma l y = 2 x^{3} - 5 x, (1, - 3)