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Beliebt Rechnen >

integral from 9 to x of sqrt(1+9t)

Lösung

\int_{9}^{x} 1 + 9 t d t

Lösung

\frac{2 ( 1 + 9 x ) ^{\frac{3}{2}} - 164 82}{27}

Schritte zur Lösung

\int_{9}^{x} 1 + 9 t d t

Wende U-Substitution an

= \int_{82}^{1 + 9 x} \frac{u}{9} d u

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int_{82}^{1 + 9 x} u d u

Wende die Potenzregel an

= \frac{1}{9} [\frac{2}{3} u^{\frac{3}{2}}]_{82}^{1 + 9 x}

Berechne die Grenzen:

\frac{2}{3} (1 + 9 x)^{\frac{3}{2}} - \frac{164 82}{3}

= \frac{1}{9} (\frac{2}{3} (1 + 9 x)^{\frac{3}{2}} - \frac{164 82}{3})

Vereinfache

= \frac{2 ( 1 + 9 x ) ^{\frac{3}{2}} - 164 82}{27}

Beliebte Beispiele

derivative of log_{e}(x^3)

\frac{d}{d x} (lo g_{e} (x^{3}))

integral from 0 to 2 of 1/8 (x+y)

\int_{0}^{2} \frac{1}{8} (x + y) d y

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