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Beliebt Rechnen >

integral of (u^2-1)/(u^2+1)

Lösung

\int \frac{u ^{2} - 1}{u ^{2} + 1} d u

Lösung

- 2 arctan (u) + u + C

Schritte zur Lösung

\int \frac{u ^{2} - 1}{u ^{2} + 1} d u

\frac{u ^{2} - 1}{u ^{2} + 1} = - \frac{2}{u ^{2} + 1} + 1

= \int - \frac{2}{u ^{2} + 1} + 1 d u

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{2}{u ^{2} + 1} d u + \int 1 d u

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

\int 1 d u = u

= - 2 arctan (u) + u

Füge eine Konstante zur Lösung hinzu

= - 2 arctan (u) + u + C

Graph

Beliebte Beispiele

tangent f(x)=5e^x,\at x=3

t an g e n t f (x) = 5 e^{x}, at x = 3

derivative of (x^3/((x+2)^2))

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

integral of 36(4x+4)^{(2)}-2sqrt((3x-1))

\int 36 (4 x + 4)^{(2)} - 2 (3 x - 1) d x

integral of cos^{-1}(x)

\int cos^{- 1} (x) d x

t an g e n t x^{2} + 9