integral of (9x-8)/((x-3)(2x-5))

Lösung

\int \frac{9 x - 8}{( x - 3 ) ( 2 x - 5 )} d x

\frac{9}{4} (ln 16 x^{2} - 88 x + 120 - 22 (\frac{ln ∣ 4 x - 10 ∣}{2} - \frac{ln ∣ 4 x - 12 ∣}{2})) - 8 (- ln ∣ 2 x - 5 ∣ + ln ∣ 2 x - 6 ∣) + C

Schritte zur Lösung

\int \frac{9 x - 8}{( x - 3 ) ( 2 x - 5 )} d x

Multipliziere aus

\frac{9 x - 8}{( x - 3 ) ( 2 x - 5 )} : \frac{9 x}{( x - 3 ) ( 2 x - 5 )} - \frac{8}{( x - 3 ) ( 2 x - 5 )}

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{9 x}{( x - 3 ) ( 2 x - 5 )} d x - \int \frac{8}{( x - 3 ) ( 2 x - 5 )} d x

\int \frac{9 x}{( x - 3 ) ( 2 x - 5 )} d x = \frac{9}{4} (ln 16 x^{2} - 88 x + 120 - 22 (\frac{ln ∣ 4 x - 10 ∣}{2} - \frac{ln ∣ 4 x - 12 ∣}{2}))

\int \frac{8}{( x - 3 ) ( 2 x - 5 )} d x = 8 (- ln ∣ 2 x - 5 ∣ + ln ∣ 2 x - 6 ∣)

= \frac{9}{4} (ln 16 x^{2} - 88 x + 120 - 22 (\frac{ln ∣ 4 x - 10 ∣}{2} - \frac{ln ∣ 4 x - 12 ∣}{2})) - 8 (- ln ∣ 2 x - 5 ∣ + ln ∣ 2 x - 6 ∣)

Füge eine Konstante zur Lösung hinzu

= \frac{9}{4} (ln 16 x^{2} - 88 x + 120 - 22 (\frac{ln ∣ 4 x - 10 ∣}{2} - \frac{ln ∣ 4 x - 12 ∣}{2})) - 8 (- ln ∣ 2 x - 5 ∣ + ln ∣ 2 x - 6 ∣) + C

\int \frac{2 x + 3}{( 2 x ^{2} + 6 x - 7 ) ^{3}} d x

\int cos (x) \cdot cos (2 x) d x

\int e^{c o s (9 x)} sin (9 x) d x

\int uv d x

\int (2 - t) t d t