integral of (x+1)(6x-5)

Lösung

\int (x + 1) (6 x - 5) d x

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

Schritte zur Lösung

\int (x + 1) (6 x - 5) d x

Wende die partielle Integration an

= (6 x - 5) (\frac{x ^{2}}{2} + x) - \int 6 (\frac{x ^{2}}{2} + x) d x

\int 6 (\frac{x ^{2}}{2} + x) d x = x^{3} + 3 x^{2}

= (6 x - 5) (\frac{x ^{2}}{2} + x) - (x^{3} + 3 x^{2})

Vereinfache

(6 x - 5) (\frac{x ^{2}}{2} + x) - (x^{3} + 3 x^{2}) : 2 x^{3} + 3 x^{2} - \frac{5 x ^{2}}{2} - 5 x

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

Füge eine Konstante zur Lösung hinzu

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

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

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

\int t^{2} cos (t) d t

d er i v a t i v e (x - 9) (x - 3)^{2}

d er i v a t i v e y = x^{5 s i n (x)}