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Beliebt Rechnen >

integral of 6xsqrt(x+5)

Lösung

\int 6 x x + 5 d x

Lösung

6 (\frac{2}{5} (x + 5)^{\frac{5}{2}} - \frac{10}{3} (x + 5)^{\frac{3}{2}}) + C

Schritte zur Lösung

\int 6 x x + 5 d x

Entferne die Konstante:

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

= 6 \cdot \int x x + 5 d x

Wende U-Substitution an

= 6 \cdot \int (u - 5) u d u

Multipliziere aus

(u - 5) u : u^{\frac{3}{2}} - 5 u

= 6 \cdot \int u^{\frac{3}{2}} - 5 u d u

Wende die Summenregel an:

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

= 6 (\int u^{\frac{3}{2}} d u - \int 5 u d u)

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

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

= 6 (\frac{2}{5} u^{\frac{5}{2}} - \frac{10}{3} u^{\frac{3}{2}})

Setze in

u = x + 5

ein

= 6 (\frac{2}{5} (x + 5)^{\frac{5}{2}} - \frac{10}{3} (x + 5)^{\frac{3}{2}})

Füge eine Konstante zur Lösung hinzu

= 6 (\frac{2}{5} (x + 5)^{\frac{5}{2}} - \frac{10}{3} (x + 5)^{\frac{3}{2}}) + C

Graph

Beliebte Beispiele

integral of xsqrt(x^2-2x+2)

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

integral of 1/(x(1+5ln(x)))

\int \frac{1}{x ( 1 + 5 ln ( x ) )} d x

integral of 1/(u^2-2)

\int \frac{1}{u ^{2} - 2} d u

integral of ((9+8x))/(1+x^2)

\int \frac{( 9 + 8 x )}{1 + x ^{2}} d x

integral of (2x^2)/2

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