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Beliebt Rechnen >

integral of 1/(xsqrt(400x^2-400))

Lösung

\int \frac{1}{x 400 x ^{2} - 400} d x

Lösung

\frac{1}{20} arctan (x^{2} - 1) + C

Schritte zur Lösung

\int \frac{1}{x 400 x ^{2} - 400} d x

Wende die partielle Integration an

= \frac{1}{20 x ^{2} - 1} - \int - \frac{2 x ^{2} - 1}{20 x ( x ^{2} - 1 ) x ^{2} - 1} d x

\int - \frac{2 x ^{2} - 1}{20 x ( x ^{2} - 1 ) x ^{2} - 1} d x = - \frac{1}{20} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))

= \frac{1}{20 x ^{2} - 1} - (- \frac{1}{20} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1)))

Vereinfache

\frac{1}{20 x ^{2} - 1} - (- \frac{1}{20} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))) : \frac{1}{20} arctan (x^{2} - 1)

= \frac{1}{20} arctan (x^{2} - 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{20} arctan (x^{2} - 1) + C

Graph

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