integral of (3-z)/(-1+z^2)

Lösung

\int \frac{3 - z}{- 1 + z ^{2}} d z

- 3 (\frac{1}{2} ln ∣ z + 1 ∣ - \frac{1}{2} ln ∣ z - 1 ∣) - \frac{1}{2} ln - 1 + z^{2} + C

Schritte zur Lösung

\int \frac{3 - z}{- 1 + z ^{2}} d z

Multipliziere aus

\frac{3 - z}{- 1 + z ^{2}} : \frac{3}{- 1 + z ^{2}} - \frac{z}{- 1 + z ^{2}}

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{3}{- 1 + z ^{2}} d z - \int \frac{z}{- 1 + z ^{2}} d z

\int \frac{3}{- 1 + z ^{2}} d z = - 3 (\frac{1}{2} ln ∣ z + 1 ∣ - \frac{1}{2} ln ∣ z - 1 ∣)

\int \frac{z}{- 1 + z ^{2}} d z = \frac{1}{2} ln - 1 + z^{2}

= - 3 (\frac{1}{2} ln ∣ z + 1 ∣ - \frac{1}{2} ln ∣ z - 1 ∣) - \frac{1}{2} ln - 1 + z^{2}

Füge eine Konstante zur Lösung hinzu

= - 3 (\frac{1}{2} ln ∣ z + 1 ∣ - \frac{1}{2} ln ∣ z - 1 ∣) - \frac{1}{2} ln - 1 + z^{2} + C

d er i v a t i v e cos (sin (5) x^{3})

\frac{d}{d x} (ln (\frac{x}{a}))

\int \frac{8 + t + t ^{2}}{t} d t

t an g e n t 8 x^{2} + 3 x

d er i v a t i v e f (x) = 2 x^{2} - x^{3}