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Beliebt Rechnen >

integral of (-4x+1)/(sqrt(1-x^2))

Lösung

\int \frac{- 4 x + 1}{1 - x ^{2}} d x

Lösung

4 1 - x^{2} + arcsin (x) + C

Schritte zur Lösung

\int \frac{- 4 x + 1}{1 - x ^{2}} d x

Multipliziere aus

\frac{- 4 x + 1}{1 - x ^{2}} : - \frac{4 x}{1 - x ^{2}} + \frac{1}{1 - x ^{2}}

= \int - \frac{4 x}{1 - x ^{2}} + \frac{1}{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{4 x}{1 - x ^{2}} d x + \int \frac{1}{1 - x ^{2}} d x

\int \frac{4 x}{1 - x ^{2}} d x = - 4 1 - x^{2}

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

= - (- 4 1 - x^{2}) + arcsin (x)

Vereinfache

= 4 1 - x^{2} + arcsin (x)

Füge eine Konstante zur Lösung hinzu

= 4 1 - x^{2} + arcsin (x) + C

Graph

Beliebte Beispiele

integral of (cos(pi/(x^{27)}))/(x^{28)}

\int \frac{cos ( \frac{π}{x ^{27}} )}{x ^{28}} d x

integral of (2x-11)/(x^3+2x^2)

\int \frac{2 x - 11}{x ^{3} + 2 x ^{2}} d x

integral of 1/(sqrt(1-3x))

\int \frac{1}{1 - 3 x} d x

integral of sqrt(1-9t^2)

\int 1 - 9 t^{2} d t

integral of (x+3)sqrt(x-1)

\int (x + 3) x - 1 d x