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Beliebt Rechnen >

integral from 5 to 6 of xsqrt(x-5)

Lösung

\int_{5}^{6} x x - 5 d x

Lösung

\frac{56}{15}

+1

Dezimale

3.73333 \dots

Schritte zur Lösung

\int_{5}^{6} x x - 5 d x

Wende U-Substitution an

= \int_{0}^{1} (u + 5) u d u

Multipliziere aus

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

= \int_{0}^{1} 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

= \int_{0}^{1} u^{\frac{3}{2}} d u + \int_{0}^{1} 5 u d u

\int_{0}^{1} u^{\frac{3}{2}} d u = \frac{2}{5}

\int_{0}^{1} 5 u d u = \frac{10}{3}

= \frac{2}{5} + \frac{10}{3}

Vereinfache

\frac{2}{5} + \frac{10}{3} : \frac{56}{15}

= \frac{56}{15}

Graph

Beliebte Beispiele

integral of (2e^{3x})/(5-4e^{3x)}

\int \frac{2 e ^{3 x}}{5 - 4 e ^{3 x}} d x

y^{'''}-12y^{''}+47y^'-66y=0

y^{^{'''}} - 12 y^{^{''}} + 47 y^{^{'}} - 66 y = 0

integral of (ln(2x^5))/(x^2)

\int \frac{ln ( 2 x ^{5} )}{x ^{2}} d x

integral of-(2000x)/(sqrt(25-x^2))

\int - \frac{2000 x}{25 - x ^{2}} d x

integral of-18x^{-19}

\int - 18 x^{- 19} d x