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Beliebt Rechnen >

integral of (4x^3+3x^2+2x+5)

Lösung

\int (4 x^{3} + 3 x^{2} + 2 x + 5) d x

Lösung

x^{4} + x^{3} + x^{2} + 5 x + C

Schritte zur Lösung

\int 4 x^{3} + 3 x^{2} + 2 x + 5 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 4 x^{3} d x + \int 3 x^{2} d x + \int 2 x d x + \int 5 d x

\int 4 x^{3} d x = x^{4}

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

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

\int 5 d x = 5 x

= x^{4} + x^{3} + x^{2} + 5 x

Füge eine Konstante zur Lösung hinzu

= x^{4} + x^{3} + x^{2} + 5 x + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(ln(x)y)

\frac{\partial}{\partial x} (ln (x) y)

integral of 5x^4sin^2(x^5)

\int 5 x^{4} sin^{2} (x^{5}) d x

(dy)/(dx)=e^{2x-5y}

\frac{d y}{d x} = e^{2 x - 5 y}

y^'=(x^2+2y^2)/(xy)

y^{^{'}} = \frac{x ^{2} + 2 y ^{2}}{x y}

y^{''}-y^'-30=0

y^{^{''}} - y^{^{'}} - 30 = 0