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Beliebt Rechnen >

integral of (3x+2e^x)^2

Lösung

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

Lösung

3 x^{3} + 12 (e^{x} x - e^{x}) + 2 e^{2 x} + C

Schritte zur Lösung

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

Multipliziere aus

(3 x + 2 e^{x})^{2} : 9 x^{2} + 12 e^{x} x + 4 e^{2 x}

= \int 9 x^{2} + 12 e^{x} x + 4 e^{2 x} 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 9 x^{2} d x + \int 12 e^{x} x d x + \int 4 e^{2 x} d x

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

\int 12 e^{x} x d x = 12 (e^{x} x - e^{x})

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

= 3 x^{3} + 12 (e^{x} x - e^{x}) + 2 e^{2 x}

Füge eine Konstante zur Lösung hinzu

= 3 x^{3} + 12 (e^{x} x - e^{x}) + 2 e^{2 x} + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(5sqrt(9x^2+16y^2))

\frac{\partial}{\partial x} (5 9 x^{2} + 16 y^{2})

integral of 7/(x(x^2+25))

\int \frac{7}{x ( x ^{2} + 25 )} d x

(d^2)/(dx^2)(sin(x^2))

\frac{d ^{2}}{d x ^{2}} (sin (x^{2}))

integral of csc^4(x)cot^2(x)

\int csc^{4} (x) cot^{2} (x) d x

limit as x approaches 2 of 5x^3+x

x \to 2 lim (5 x^{3} + x)