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Beliebt Rechnen >

integral of 2x^4+e^{2x}+sin(3x)

Lösung

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

Lösung

\frac{2 x ^{5}}{5} + \frac{1}{2} e^{2 x} - \frac{1}{3} cos (3 x) + C

Schritte zur Lösung

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

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

= \frac{2 x ^{5}}{5} + \frac{1}{2} e^{2 x} - \frac{1}{3} cos (3 x)

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{5}}{5} + \frac{1}{2} e^{2 x} - \frac{1}{3} cos (3 x) + C

Graph

Beliebte Beispiele

derivative f(x)= 4/(1+x^2)

d er i v a t i v e f (x) = \frac{4}{1 + x ^{2}}

integral of x^2*e^{2x}

\int x^{2} \cdot e^{2 x} d x

y^{^{'}} = 1 + x - y - x y

limit as x approaches 2 of (sin(2x))/x

x \to 2 lim (\frac{sin ( 2 x )}{x})

tangent y=sqrt(x)(81.9)

t an g e n t y = x (81.9)