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Beliebt Rechnen >

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

Lösung

\int \frac{x ^{4} + x}{x} d x

Lösung

\frac{2}{9} x^{\frac{9}{2}} + \frac{2}{3} x^{\frac{3}{2}} + C

Schritte zur Lösung

\int \frac{x ^{4} + x}{x} d x

Vereinfache

\frac{x ^{4} + x}{x} : x (x^{3} + 1)

= \int x (x^{3} + 1) d x

Multipliziere aus

x (x^{3} + 1) : x^{\frac{7}{2}} + x

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

\int x^{\frac{7}{2}} d x = \frac{2}{9} x^{\frac{9}{2}}

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

= \frac{2}{9} x^{\frac{9}{2}} + \frac{2}{3} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{9} x^{\frac{9}{2}} + \frac{2}{3} x^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of (sin(1/(x^5)))/(x^6)

\int \frac{sin ( \frac{1}{x ^{5}} )}{x ^{6}} d x

integral of xsqrt(2+x^2)

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

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

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

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\int \frac{1}{( e ^{x} + 1 ) ^{2}} d x

integral of 1/(2+sin^2(x))

\int \frac{1}{2 + sin ^{2} ( x )} d x