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Beliebt Rechnen >

integral of (5-50x)/(sqrt(1-25x^2))

Lösung

\int \frac{5 - 50 x}{1 - 25 x ^{2}} d x

Lösung

arcsin (5 x) + 2 1 - 25 x^{2} + C

Schritte zur Lösung

\int \frac{5 - 50 x}{1 - 25 x ^{2}} d x

Multipliziere aus

\frac{5 - 50 x}{1 - 25 x ^{2}} : \frac{5}{1 - 25 x ^{2}} - \frac{50 x}{1 - 25 x ^{2}}

= \int \frac{5}{1 - 25 x ^{2}} - \frac{50 x}{1 - 25 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{5}{1 - 25 x ^{2}} d x - \int \frac{50 x}{1 - 25 x ^{2}} d x

\int \frac{5}{1 - 25 x ^{2}} d x = arcsin (5 x)

\int \frac{50 x}{1 - 25 x ^{2}} d x = - 2 1 - 25 x^{2}

= arcsin (5 x) - (- 2 1 - 25 x^{2})

Vereinfache

= arcsin (5 x) + 2 1 - 25 x^{2}

Füge eine Konstante zur Lösung hinzu

= arcsin (5 x) + 2 1 - 25 x^{2} + C

Graph

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