integral of x^4-4x^2+4

Lösung

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

\frac{x ^{5}}{5} - \frac{4 x ^{3}}{3} + 4 x + C

Schritte zur Lösung

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

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 4 d x = 4 x

= \frac{x ^{5}}{5} - \frac{4 x ^{3}}{3} + 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} - \frac{4 x ^{3}}{3} + 4 x + C

\int (4 x + 3) (2 x^{2} + 3 x)^{2} d x

\int \frac{12 x + 24}{x ^{2} + 4 x + 3} d x

d er i v a t i v e 3 x + 2

\frac{d}{d x} (\frac{( 3 - 5 x ) ^{6}}{10})

\int \frac{3 \cdot 2 ^{x} - 2 \cdot 3 ^{x}}{2 ^{x}} d x