integral-6x^3+9x^2+4x-3

Lösung

integral

- 6 x^{3} + 9 x^{2} + 4 x - 3

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

Schritte zur Lösung

\int - 6 x^{3} + 9 x^{2} + 4 x - 3 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 6 x^{3} d x + \int 9 x^{2} d x + \int 4 x d x - \int 3 d x

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int 9 x^{2} d x = 3 x^{3}

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

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

in t e g r a l 3 x^{2} + 4 x

in t e g r a l cos^{2} (3 x)

in t e g r a l \frac{1 + e ^{- x}}{e ^{x}}

in t e g r a l \frac{x ^{2}}{e ^{x}}

in t e g r a l (x + 2)^{5}