integral of (7x^5+6x^4-3x^3-9x+5)

Lösung

\int (7 x^{5} + 6 x^{4} - 3 x^{3} - 9 x + 5) d x

\frac{7 x ^{6}}{6} + \frac{6 x ^{5}}{5} - \frac{3 x ^{4}}{4} - \frac{9 x ^{2}}{2} + 5 x + C

Schritte zur Lösung

\int 7 x^{5} + 6 x^{4} - 3 x^{3} - 9 x + 5 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 7 x^{5} d x + \int 6 x^{4} d x - \int 3 x^{3} d x - \int 9 x d x + \int 5 d x

\int 7 x^{5} d x = \frac{7 x ^{6}}{6}

\int 6 x^{4} d x = \frac{6 x ^{5}}{5}

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

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 5 d x = 5 x

= \frac{7 x ^{6}}{6} + \frac{6 x ^{5}}{5} - \frac{3 x ^{4}}{4} - \frac{9 x ^{2}}{2} + 5 x

Füge eine Konstante zur Lösung hinzu

= \frac{7 x ^{6}}{6} + \frac{6 x ^{5}}{5} - \frac{3 x ^{4}}{4} - \frac{9 x ^{2}}{2} + 5 x + C

\int \frac{x ^{2} - 64}{x ( x - 1 ) ^{2}} d x

\int \frac{1}{y 1 + ( ln ( y ) ) ^{2}} d y

d er i v a t i v e y = \frac{( x ^{2} + 1 )}{( x ^{3} - 1 )}

\int sec (t) (8 sec (t) + 5 tan (t)) d t

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