integral of 1/(xsqrt(121x^2-121))

Lösung

\int \frac{1}{x 121 x ^{2} - 121} d x

\frac{1}{11} arctan (x^{2} - 1) + C

Schritte zur Lösung

\int \frac{1}{x 121 x ^{2} - 121} d x

Wende die partielle Integration an

= \frac{1}{11 x ^{2} - 1} - \int - \frac{2 x ^{2} - 1}{11 x ( x ^{2} - 1 ) x ^{2} - 1} d x

\int - \frac{2 x ^{2} - 1}{11 x ( x ^{2} - 1 ) x ^{2} - 1} d x = - \frac{1}{11} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))

= \frac{1}{11 x ^{2} - 1} - (- \frac{1}{11} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1)))

Vereinfache

\frac{1}{11 x ^{2} - 1} - (- \frac{1}{11} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))) : \frac{1}{11} arctan (x^{2} - 1)

= \frac{1}{11} arctan (x^{2} - 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{11} arctan (x^{2} - 1) + C

\int y + x d x

\frac{\partial}{\partial x} (in (x + 2 y + 3 z))

\int \frac{( ln ( x ) ) ^{48}}{x} d x

d er i v a t i v e ln (3 - 5 x)

\frac{d}{d x} (\frac{3 tan ( x )}{x})