integral from 1 to 5 of ((ln(y))/(xy))

Lösung

\int_{1}^{5} (\frac{ln ( y )}{x y}) d y

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

Schritte zur Lösung

\int_{1}^{5} \frac{ln ( y )}{x y} d y

Entferne die Konstante:

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

= \frac{1}{x} \cdot \int_{1}^{5} \frac{ln ( y )}{y} d y

Wende U-Substitution an

= \frac{1}{x} \cdot \int_{0}^{l n (5)} u d u

Wende die Potenzregel an

= \frac{1}{x} [\frac{u ^{2}}{2}]_{0}^{l n (5)}

Berechne die Grenzen:

\frac{ln ^{2} ( 5 )}{2}

= \frac{1}{x} \cdot \frac{ln ^{2} ( 5 )}{2}

Vereinfache

= \frac{ln ^{2} ( 5 )}{2 x}

\int_{x^{3}}^{x^{5}} (4 t + 4)^{6} d t

\int_{0}^{4} (1 + x) d x

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\int_{0}^{1} 4 (1 - y)^{3} d y

\int_{0}^{\infty} - 3 e^{- x} d x