integral of 10x^4-4x^2-14x+12

Lösung

\int 10 x^{4} - 4 x^{2} - 14 x + 12 d x

2 x^{5} - \frac{4 x ^{3}}{3} - 7 x^{2} + 12 x + C

Schritte zur Lösung

\int 10 x^{4} - 4 x^{2} - 14 x + 12 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 10 x^{4} d x - \int 4 x^{2} d x - \int 14 x d x + \int 12 d x

\int 10 x^{4} d x = 2 x^{5}

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

\int 14 x d x = 7 x^{2}

\int 12 d x = 12 x

= 2 x^{5} - \frac{4 x ^{3}}{3} - 7 x^{2} + 12 x

Füge eine Konstante zur Lösung hinzu

= 2 x^{5} - \frac{4 x ^{3}}{3} - 7 x^{2} + 12 x + C

\int - 6 sin (x) + 7 cos (x) d x

\int csc^{2} (a x) d x

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

\int \frac{1}{( arctan ( \frac{y}{4} ) ) ( 16 + y ^{2} )} d y

\int 2 - 4 x d x