integral of (5x^2+3x-10)

Lösung

\int (5 x^{2} + 3 x - 10) d x

\frac{5 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 10 x + C

Schritte zur Lösung

\int 5 x^{2} + 3 x - 10 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 x^{2} d x + \int 3 x d x - \int 10 d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 10 d x = 10 x

= \frac{5 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 10 x

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 10 x + C

\int \frac{18 x ^{2}}{x ^{4} - 41 x ^{2} + 400} d x

\frac{d}{d x} (4 x - x^{2} - 3)

y \to 15 lim (y + 3)

\int \frac{sin ( 2 e ^{- 4 x} )}{e ^{4 x}} d x

a re a f (x) = x^{3} - 3 x^{2} + 3 x, g (x) = x