integral of (3x-4)(2x+3)

Lösung

\int (3 x - 4) (2 x + 3) d x

2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x + C

Schritte zur Lösung

\int (3 x - 4) (2 x + 3) d x

Wende die partielle Integration an

= 3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - \int 3 x^{2} - 8 x d x

\int 3 x^{2} - 8 x d x = x^{3} - 4 x^{2}

= 3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - (x^{3} - 4 x^{2})

Vereinfache

3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - (x^{3} - 4 x^{2}) : 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x

= 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x

Füge eine Konstante zur Lösung hinzu

= 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x + C

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

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

\int e^{2 x} + e^{- 2 x} + 2 d x

\int \frac{t}{t ^{2} + 2 t - 3} d t

\int \frac{3 x ^{2}}{( x - 3 ) ( x ^{2} + 1 )} d x