integral of (9x+2)^2

Lösung

\int (9 x + 2)^{2} d x

27 x^{3} + 18 x^{2} + 4 x + C

Schritte zur Lösung

\int (9 x + 2)^{2} d x

Multipliziere aus

(9 x + 2)^{2} : 81 x^{2} + 36 x + 4

= \int 81 x^{2} + 36 x + 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 81 x^{2} d x + \int 36 x d x + \int 4 d x

\int 81 x^{2} d x = 27 x^{3}

\int 36 x d x = 18 x^{2}

\int 4 d x = 4 x

= 27 x^{3} + 18 x^{2} + 4 x

Füge eine Konstante zur Lösung hinzu

= 27 x^{3} + 18 x^{2} + 4 x + C

\int \frac{a + b x ^{5}}{6 a x + b x ^{6}} d x

y^{^{''}} + 4 y^{^{'}} - 24 y = 0

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

d er i v a t i v e g (x) = \frac{1}{x}

in v erse l a pl a ce \frac{6}{s} + \frac{16}{s ^{2} + 16}