integral of (1+x)/(sqrt(1-x^2))

Lösung

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

arcsin (x) - 1 - x^{2} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{1 + x}{1 - x ^{2}} : \frac{1}{1 - x ^{2}} + \frac{x}{1 - x ^{2}}

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

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

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

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

= arcsin (x) - 1 - x^{2}

Füge eine Konstante zur Lösung hinzu

= arcsin (x) - 1 - x^{2} + C

t an g e n t \frac{2}{3 x + 1}

\frac{\partial}{\partial y} (2 - y - x^{2})

\int 9 x^{5} e^{x^{6}} d x

im pl i c i t \frac{d y}{d x}, x^{2} - x y + y^{2} = 19

\frac{\partial}{\partial x} (\frac{5 s - 3 t}{4 s + 5 t})