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Beliebt Rechnen >

integral of (8-128x)/(sqrt(1-64x^2))

Lösung

\int \frac{8 - 128 x}{1 - 64 x ^{2}} d x

Lösung

arcsin (8 x) + 2 1 - 64 x^{2} + C

Schritte zur Lösung

\int \frac{8 - 128 x}{1 - 64 x ^{2}} d x

Multipliziere aus

\frac{8 - 128 x}{1 - 64 x ^{2}} : \frac{8}{1 - 64 x ^{2}} - \frac{128 x}{1 - 64 x ^{2}}

= \int \frac{8}{1 - 64 x ^{2}} - \frac{128 x}{1 - 64 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{8}{1 - 64 x ^{2}} d x - \int \frac{128 x}{1 - 64 x ^{2}} d x

\int \frac{8}{1 - 64 x ^{2}} d x = arcsin (8 x)

\int \frac{128 x}{1 - 64 x ^{2}} d x = - 2 1 - 64 x^{2}

= arcsin (8 x) - (- 2 1 - 64 x^{2})

Vereinfache

= arcsin (8 x) + 2 1 - 64 x^{2}

Füge eine Konstante zur Lösung hinzu

= arcsin (8 x) + 2 1 - 64 x^{2} + C

Graph

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\int \frac{7}{x ^{2} + 25} d x

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\frac{d}{d x} (4 x^{\frac{2}{3}} + x^{\frac{5}{3}})

tangent f(x)=x^3-2x,\at x=2

t an g e n t f (x) = x^{3} - 2 x, at x = 2