integral of 20x^3+12x^2+4

Lösung

\int 20 x^{3} + 12 x^{2} + 4 d x

5 x^{4} + 4 x^{3} + 4 x + C

Schritte zur Lösung

\int 20 x^{3} + 12 x^{2} + 4 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 20 x^{3} d x + \int 12 x^{2} d x + \int 4 d x

\int 20 x^{3} d x = 5 x^{4}

\int 12 x^{2} d x = 4 x^{3}

\int 4 d x = 4 x

= 5 x^{4} + 4 x^{3} + 4 x

Füge eine Konstante zur Lösung hinzu

= 5 x^{4} + 4 x^{3} + 4 x + C

\frac{\partial}{\partial x} (y^{2} x + y)

\frac{d y}{d x} + y^{3} x + 5 y = 0

6 x (\frac{d y}{d x}) = 2 x e^{x} - 6 y + 6 x^{2}

\int \frac{sin ( 6 e ^{- 5 x} )}{e ^{5 x}} d x

n = 1 \sum \infty n^{4} (1 + n^{5})^{2}