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Beliebt Rechnen >

integral of 7v(v^2+4)^2

Lösung

\int 7 v (v^{2} + 4)^{2} d v

Lösung

7 (\frac{v ^{6}}{6} + 2 v^{4} + 8 v^{2}) + C

Schritte zur Lösung

\int 7 v (v^{2} + 4)^{2} d v

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int v (v^{2} + 4)^{2} d v

Multipliziere aus

v (v^{2} + 4)^{2} : v^{5} + 8 v^{3} + 16 v

= 7 \cdot \int v^{5} + 8 v^{3} + 16 v d v

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 7 (\int v^{5} d v + \int 8 v^{3} d v + \int 16 v d v)

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

\int 8 v^{3} d v = 2 v^{4}

\int 16 v d v = 8 v^{2}

= 7 (\frac{v ^{6}}{6} + 2 v^{4} + 8 v^{2})

Füge eine Konstante zur Lösung hinzu

= 7 (\frac{v ^{6}}{6} + 2 v^{4} + 8 v^{2}) + C

Graph

Beliebte Beispiele

integral of sqrt(2+2sin(x))

\int 2 + 2 sin (x) d x

integral of 2+1/x

\int 2 + \frac{1}{x} d x

tangent f(x)=(-8x)/(x^2+1),\at x=1

t an g e n t f (x) = \frac{- 8 x}{x ^{2} + 1}, at x = 1

(\partial)/(\partial x)(2x^2y+4)

\frac{\partial}{\partial x} (2 x^{2} y + 4)

steigung (0,2),(1,0)

s l o p e (0, 2), (1, 0)