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Beliebt Rechnen >

integral from 0 to 1 of 1/(x^2-2x-3)

Lösung

\int_{0}^{1} \frac{1}{x ^{2} - 2 x - 3} d x

Lösung

- \frac{1}{4} ln (3)

+1

Dezimale

- 0.27465 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1}{x ^{2} - 2 x - 3} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} - 2 x - 3} : - \frac{1}{4 ( x + 1 )} + \frac{1}{4 ( x - 3 )}

= \int_{0}^{1} - \frac{1}{4 ( x + 1 )} + \frac{1}{4 ( x - 3 )} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{1} \frac{1}{4 ( x + 1 )} d x + \int_{0}^{1} \frac{1}{4 ( x - 3 )} d x

\int_{0}^{1} \frac{1}{4 ( x + 1 )} d x = \frac{1}{4} ln (2)

\int_{0}^{1} \frac{1}{4 ( x - 3 )} d x = \frac{1}{4} (ln (2) - ln (3))

= - \frac{1}{4} ln (2) + \frac{1}{4} (ln (2) - ln (3))

Vereinfache

- \frac{1}{4} ln (2) + \frac{1}{4} (ln (2) - ln (3)) : - \frac{1}{4} ln (3)

= - \frac{1}{4} ln (3)

Graph

Beliebte Beispiele

integral from-1 to 4 of x^2

\int_{- 1}^{4} x^{2} d x

integral from 0 to 3 of (2-x)

\int_{0}^{3} (2 - x) d x

integral from-2 to 2 of x^3+x

\int_{- 2}^{2} x^{3} + x d x

integral from 1 to 3 of 3x(x^2+5)

\int_{1}^{3} 3 x (x^{2} + 5) d x

integral from 0 to 1 of (x^2)^2

\int_{0}^{1} (x^{2})^{2} d x