integral of (3-2x)/(sqrt(1-x^2))

Lösung

\int \frac{3 - 2 x}{1 - x ^{2}} d x

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

Schritte zur Lösung

\int \frac{3 - 2 x}{1 - x ^{2}} d x

Multipliziere aus

\frac{3 - 2 x}{1 - x ^{2}} : \frac{3}{1 - x ^{2}} - \frac{2 x}{1 - x ^{2}}

= \int \frac{3}{1 - x ^{2}} - \frac{2 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{3}{1 - x ^{2}} d x - \int \frac{2 x}{1 - x ^{2}} d x

\int \frac{3}{1 - x ^{2}} d x = 3 arcsin (x)

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

= 3 arcsin (x) - (- 2 1 - x^{2})

Vereinfache

= 3 arcsin (x) + 2 1 - x^{2}

Füge eine Konstante zur Lösung hinzu

= 3 arcsin (x) + 2 1 - x^{2} + C

\int (4 x^{5} + 5 x^{3} + 11) d x

\int \frac{8 x}{x ^{2} - 4} d x

\int \frac{1}{3 + 3 x ^{2}} d x

\int \frac{1}{x 25 + x ^{2}} d x

\int e^{x} + e^{5 x} d x