integral (arctan(x))/(x^2)

Lösung

integral

\frac{arctan ( x )}{x ^{2}}

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

Schritte zur Lösung

\int \frac{arctan ( x )}{x ^{2}} d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

in t e g r a l \frac{1}{( x - 2 ) ^{3} ( x + 4 ) ^{4}}

in t e g r a l (1 + x tan (x) - sin (x)) sec^{2} (x)

in t e g r a l cos^{2} (x) - sin^{2} (x)

in t e g r a l 5 + 2 x

in t e g r a l \frac{( x - 1 )}{( x + 1 )}