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Beliebt Rechnen >

integral from a to 2a of (ax-(a^3)/x)

Lösung

\int_{a}^{2 a} (a x - \frac{a ^{3}}{x}) d x

Lösung

a (2 a^{2} - \frac{a ^{2}}{2}) - ln (2) a^{3}

Schritte zur Lösung

\int_{a}^{2 a} a x - \frac{a ^{3}}{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_{a}^{2 a} a x d x - \int_{a}^{2 a} \frac{a ^{3}}{x} d x

\int_{a}^{2 a} a x d x = a (2 a^{2} - \frac{a ^{2}}{2})

\int_{a}^{2 a} \frac{a ^{3}}{x} d x = ln (2) a^{3}

= a (2 a^{2} - \frac{a ^{2}}{2}) - ln (2) a^{3}

Beliebte Beispiele

limit as x approaches infinity of 4e^{-4x}

x \to \infty lim (4 e^{- 4 x})

integral of x^{6/5}

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

integral from 1 to 3 of 3(2^{x+1})

\int_{1}^{3} 3 (2^{x + 1}) d x

(dy)/(dx)=x^6y^{-3},y(0)=4

\frac{d y}{d x} = x^{6} y^{- 3}, y (0) = 4

f(x)=x^{log_{10}(x)}

f (x) = x^{l o g_{10} (x)}