integral of 5-3x^3+2x^2

Lösung

\int 5 - 3 x^{3} + 2 x^{2} d x

5 x - \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3} + C

Schritte zur Lösung

\int 5 - 3 x^{3} + 2 x^{2} 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 5 d x - \int 3 x^{3} d x + \int 2 x^{2} d x

\int 5 d x = 5 x

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

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

= 5 x - \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= 5 x - \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3} + C

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

\int \frac{4 x ^{3} - 2 x ^{2} + 5}{x ^{2} - x - 6} d x

\int 10 (20 - x) e^{- \frac{x}{20}} d x

\int t^{3} - \frac{e ^{- t} - 4}{e ^{- t}} d t

\int (tan (x))^{\frac{1}{3}} sec^{4} (x) d x