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

Lösung

\int (2 x - 5) (3 x + 2) d x

2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x + C

Schritte zur Lösung

\int (2 x - 5) (3 x + 2) d x

Wende die partielle Integration an

= 3 x^{3} + 4 x^{2} - \frac{15 x ^{2}}{2} - 10 x - \int 3 x^{2} + 4 x d x

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

= 3 x^{3} + 4 x^{2} - \frac{15 x ^{2}}{2} - 10 x - (x^{3} + 2 x^{2})

Vereinfache

3 x^{3} + 4 x^{2} - \frac{15 x ^{2}}{2} - 10 x - (x^{3} + 2 x^{2}) : 2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x

= 2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x

Füge eine Konstante zur Lösung hinzu

= 2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x + C

\int (e^{- 3 t} + cos (2 t)) d t

\int \frac{6 x ^{3} + 1}{x ^{2}} d x

\int 5 x x^{2} - 1 d x

\int y 4 + y^{2} d y

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