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Beliebt Rechnen >

integral of (0.8x+1/(60^2))^{-1/2}

Lösung

\int (0.8 x + \frac{1}{6 0 ^{2}})^{- \frac{1}{2}} d x

Lösung

2.5 (0.8 x + 0.00027 \dots)^{\frac{1}{2}} + C

Schritte zur Lösung

\int (0.8 x + \frac{1}{6 0 ^{2}})^{- \frac{1}{2}} d x

Wende U-Substitution an

= \int \frac{1}{0.8 u ^{\frac{1}{2}}} d u

Entferne die Konstante:

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

= \frac{1}{0.8} \cdot \int \frac{1}{u ^{\frac{1}{2}}} d u

Vereinfache

= 1.25 \cdot \int \frac{1}{u ^{\frac{1}{2}}} d u

Wende die Potenzregel an

= 1.25 \cdot 2 u^{\frac{1}{2}}

Setze in

u = 0.8 x + \frac{1}{6 0 ^{2}}

ein

= 1.25 \cdot 2 (0.8 x + \frac{1}{6 0 ^{2}})^{\frac{1}{2}}

Vereinfache

= 2.5 (0.8 x + 0.00027 \dots)^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= 2.5 (0.8 x + 0.00027 \dots)^{\frac{1}{2}} + C

Graph

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