integral of (t^3-1)/(2t-2)

Lösung

\int \frac{t ^{3} - 1}{2 t - 2} d t

\frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{1}{2} t + C

Schritte zur Lösung

\int \frac{t ^{3} - 1}{2 t - 2} d t

Multipliziere aus

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

= \int \frac{t ^{2}}{2} + \frac{t}{2} + \frac{1}{2} d t

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{t ^{2}}{2} d t + \int \frac{t}{2} d t + \int \frac{1}{2} d t

\int \frac{t ^{2}}{2} d t = \frac{t ^{3}}{6}

\int \frac{t}{2} d t = \frac{t ^{2}}{4}

\int \frac{1}{2} d t = \frac{1}{2} t

= \frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{1}{2} t

Füge eine Konstante zur Lösung hinzu

= \frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{1}{2} t + C

d er i v a t i v e 5 x^{4} (3 x - 7)

\int \frac{4}{7 x + 5} d x

x \to 2 lim (cos (\frac{1}{x - 2}))

\int cos (3 x) cos (4 x) d x

d er i v a t i v e g (x) = (1 - x^{2})^{- x}