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Beliebt Rechnen >

integral (t^2)/((1-t^2))

Lösung

integral

\frac{t ^{2}}{( 1 - t ^{2} )}

Lösung

\frac{ln ∣ t + 1 ∣}{2} - \frac{ln ∣ t - 1 ∣}{2} - t + C

Schritte zur Lösung

\int \frac{t ^{2}}{1 - t ^{2}} d t

\frac{t ^{2}}{1 - t ^{2}} = \frac{1}{1 - t ^{2}} - 1

= \int \frac{1}{1 - t ^{2}} - 1 d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{1 - t ^{2}} d t - \int 1 d t

\int \frac{1}{1 - t ^{2}} d t = \frac{ln ∣ t + 1 ∣}{2} - \frac{ln ∣ t - 1 ∣}{2}

\int 1 d t = t

= \frac{ln ∣ t + 1 ∣}{2} - \frac{ln ∣ t - 1 ∣}{2} - t

Füge eine Konstante zur Lösung hinzu

= \frac{ln ∣ t + 1 ∣}{2} - \frac{ln ∣ t - 1 ∣}{2} - t + C

Graph

Beliebte Beispiele

integral 1/((a-x))

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

integral 8/((x^3-16x))

in t e g r a l \frac{8}{( x ^{3} - 16 x )}

integral x/((x+1))

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

in t e g r a l 3 x^{3}

integral x/((x^2+y^2))

in t e g r a l \frac{x}{( x ^{2} + y ^{2} )}