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

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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

\frac{d}{d x} ((3 - 2 x)^{2})

t an g e n t f (x) = \frac{2 x}{x ^{2} + 1}, (- 1, - 1)

s im pl i f y \frac{2 ( x + 1 )}{x ^{2} + 1}

d er i v a t i v e r^{2} - 9 x^{2}