integral 1/(((x-3)(x+7)))

Lösung

integral

\frac{1}{( ( x - 3 ) ( x + 7 ) )}

\frac{1}{10} ln ∣ x - 3 ∣ - \frac{1}{10} ln ∣ x + 7 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x - 3 ) ( x + 7 )} d x

Ermittle den Partialbruch von

\frac{1}{( x - 3 ) ( x + 7 )} : \frac{1}{10 ( x - 3 )} - \frac{1}{10 ( x + 7 )}

= \int \frac{1}{10 ( x - 3 )} - \frac{1}{10 ( x + 7 )} 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 \frac{1}{10 ( x - 3 )} d x - \int \frac{1}{10 ( x + 7 )} d x

\int \frac{1}{10 ( x - 3 )} d x = \frac{1}{10} ln ∣ x - 3 ∣

\int \frac{1}{10 ( x + 7 )} d x = \frac{1}{10} ln ∣ x + 7 ∣

= \frac{1}{10} ln ∣ x - 3 ∣ - \frac{1}{10} ln ∣ x + 7 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{10} ln ∣ x - 3 ∣ - \frac{1}{10} ln ∣ x + 7 ∣ + C

in t e g r a l - 5 cos (\frac{x}{2})

in t e g r a l e^{(x^{2}) - x}

in t e g r a l \frac{1}{( x ^{2} + a ) ^{2}}

in t e g r a l \frac{sin ^{2} ( 2 x )}{cos ^{2} ( x )}

in t e g r a l \frac{( x + 2 )}{( x ^{2} + 1 )}