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Beliebt Rechnen >

integral of x(x^4+1/4 x)

Lösung

\int x (x^{4} + \frac{1}{4} x) d x

Lösung

\frac{x ^{6}}{6} + \frac{x ^{3}}{12} + C

Schritte zur Lösung

\int x (x^{4} + \frac{1}{4} x) d x

Multipliziere aus

x (x^{4} + \frac{1}{4} x) : x^{5} + \frac{x ^{2}}{4}

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

\int x^{5} d x = \frac{x ^{6}}{6}

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

= \frac{x ^{6}}{6} + \frac{x ^{3}}{12}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} + \frac{x ^{3}}{12} + C

Graph

Beliebte Beispiele

integral of y^3e^{y^4}

\int y^{3} e^{y^{4}} d y

derivative of cos((pix^9))

\frac{d}{d x} (cos ((π x)^{9}))

(\partial)/(\partial x)(x^{0.1})

\frac{\partial}{\partial x} (x^{0.1})

integral of (1-x)^2sqrt(x)

\int (1 - x)^{2} x d x

y^{''}-10y^'+25y=0,y(0)=7,y^'(0)=0

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 7, y^{^{'}} (0) = 0