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Beliebt Rechnen >

integral of x^5+5sqrt(x)

Lösung

\int x^{5} + 5 x d x

Lösung

\frac{x ^{6}}{6} + \frac{10}{3} x^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{5} + 5 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^{5} d x + \int 5 x d x

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

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

= \frac{x ^{6}}{6} + \frac{10}{3} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} + \frac{10}{3} x^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of (ax+b)^2

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

integral of 10x(ln(x))^2

\int 10 x (ln (x))^{2} d x

integral of (5x^2+6)^2

\int (5 x^{2} + 6)^{2} d x

integral of (x^3+1)^{10}

\int (x^{3} + 1)^{10} d x

integral of ((a+bx^8))/(sqrt(9ax+bx^9))

\int \frac{( a + b x ^{8} )}{9 a x + b x ^{9}} d x