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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2}{7} x^{\frac{7}{2}} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int x^{\frac{5}{2}} d x = \frac{2}{7} x^{\frac{7}{2}}

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

= \frac{2}{7} x^{\frac{7}{2}} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} x^{\frac{7}{2}} + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

integral of x(a-bx^2)

\int x (a - b x^{2}) d x

tangent f(x)=2x^2+x-2,\at x=4

t an g e n t f (x) = 2 x^{2} + x - 2, at x = 4

integral of (-1600x)/(sqrt(25-x^2))

\int \frac{- 1600 x}{25 - x ^{2}} d x

integral of 1/(xsqrt(8x+81))

\int \frac{1}{x 8 x + 81} d x

(\partial)/(\partial x)(x+e^y)

\frac{\partial}{\partial x} (x + e^{y})