integral from 1 to e^2 of ((in(x))^2)/x

Lösung

\int_{1}^{e^{2}} \frac{( in ( x ) ) ^{2}}{x} d x

\frac{e ^{4} i ^{2} n ^{2} - i ^{2} n ^{2}}{2}

Schritte zur Lösung

\int_{1}^{e^{2}} \frac{( in x ) ^{2}}{x} d x

Wende die partielle Integration an

= [i^{2} n^{2} x^{2} - \int i^{2} n^{2} x d x]_{1}^{e^{2}}

\int i^{2} n^{2} x d x = \frac{i ^{2} n ^{2} x ^{2}}{2}

= [i^{2} n^{2} x^{2} - \frac{i ^{2} n ^{2} x ^{2}}{2}]_{1}^{e^{2}}

Füge

i^{2} n^{2} x^{2} - \frac{i ^{2} n ^{2} x ^{2}}{2}

zusammen:

\frac{i ^{2} n ^{2} x ^{2}}{2}

= [\frac{i ^{2} n ^{2} x ^{2}}{2}]_{1}^{e^{2}}

Berechne die Grenzen:

\frac{e ^{4} i ^{2} n ^{2}}{2} - \frac{i ^{2} n ^{2}}{2}

= \frac{e ^{4} i ^{2} n ^{2}}{2} - \frac{i ^{2} n ^{2}}{2}

Vereinfache

= \frac{e ^{4} i ^{2} n ^{2} - i ^{2} n ^{2}}{2}

\int_{0}^{1} \frac{- x ^{2} + x}{x + 1} d x

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