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Beliebt Rechnen >

integral of (ln(1+x^2))/(x^2)

Lösung

\int \frac{ln ( 1 + x ^{2} )}{x ^{2}} d x

Lösung

- \frac{ln ( 1 + x ^{2} )}{x} + 2 arctan (x) + C

Schritte zur Lösung

\int \frac{ln ( 1 + x ^{2} )}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{ln ( 1 + x ^{2} )}{x} - \int - \frac{2}{1 + x ^{2}} d x

\int - \frac{2}{1 + x ^{2}} d x = - 2 arctan (x)

= - \frac{ln ( 1 + x ^{2} )}{x} - (- 2 arctan (x))

Vereinfache

= - \frac{ln ( 1 + x ^{2} )}{x} + 2 arctan (x)

Füge eine Konstante zur Lösung hinzu

= - \frac{ln ( 1 + x ^{2} )}{x} + 2 arctan (x) + C

Graph

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2y^{''}+20y^'+50y=0

2 y^{^{''}} + 20 y^{^{'}} + 50 y = 0

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\frac{\partial}{\partial x} (2 x^{2} + y^{2})

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n = 1 \sum \infty (\frac{1}{2})^{99 - 1}

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