integral of (3x^3+4x^2-2x^{-1}+13)

Lösung

\int (3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13) d x

\frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x + C

Schritte zur Lösung

\int 3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13 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 3 x^{3} d x + \int 4 x^{2} d x - \int 2 x^{- 1} d x + \int 13 d x

\int 3 x^{3} d x = \frac{3 x ^{4}}{4}

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 2 x^{- 1} d x = 2 ln ∣ x ∣

\int 13 d x = 13 x

= \frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x + C

l a pl a ce t r an s f or m t^{2} cos (5 t)

d er i v a t i v e \frac{sin ( x )}{2 + cos ( x )}

t a y l or sin (5 x), x = 0

d er i v a t i v e \frac{1}{ln ( x + 1 )}

\frac{\partial}{\partial y} (5 x + y)