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Beliebt Rechnen >

integral of (sqrt(16+x^2))/(2x^4)

Lösung

\int \frac{16 + x ^{2}}{2 x ^{4}} d x

Lösung

\frac{1}{2} (- \frac{16 + x ^{2}}{3 x ^{3}} - \frac{16 + x ^{2}}{48 x}) + C

Schritte zur Lösung

\int \frac{16 + x ^{2}}{2 x ^{4}} d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int \frac{16 + x ^{2}}{x ^{4}} d x

Wende die partielle Integration an

= \frac{1}{2} (- \frac{16 + x ^{2}}{3 x ^{3}} - \int - \frac{1}{3 x ^{2} x ^{2} + 16} d x)

\int - \frac{1}{3 x ^{2} x ^{2} + 16} d x = \frac{16 + x ^{2}}{48 x}

= \frac{1}{2} (- \frac{16 + x ^{2}}{3 x ^{3}} - \frac{16 + x ^{2}}{48 x})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (- \frac{16 + x ^{2}}{3 x ^{3}} - \frac{16 + x ^{2}}{48 x}) + C

Graph

Beliebte Beispiele

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n = 1 \sum \infty (x + 1)^{n}

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x \to - \infty lim (- 18 x^{4})