integral of 1/(xsqrt(256x^2-256))

Lösung

\int \frac{1}{x 256 x ^{2} - 256} d x

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

Schritte zur Lösung

\int \frac{1}{x 256 x ^{2} - 256} d x

Wende die partielle Integration an

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

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

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

Vereinfache

\frac{1}{16 x ^{2} - 1} - (- \frac{1}{16} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))) : \frac{1}{16} arctan (x^{2} - 1)

= \frac{1}{16} arctan (x^{2} - 1)

Füge eine Konstante zur Lösung hinzu

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

x \to 1 - lim ((x - 1)^{2} f (x))

d er i v a t i v e cot (x^{7})

x \to 2 lim (x 8 - x^{2})

\int \frac{1}{16 x ^{2} - 25} d x

\frac{d}{d x} (π)