de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (3-18x)/(sqrt(1-9x^2))

Lösung

\int \frac{3 - 18 x}{1 - 9 x ^{2}} d x

Lösung

arcsin (3 x) + 2 1 - 9 x^{2} + C

Schritte zur Lösung

\int \frac{3 - 18 x}{1 - 9 x ^{2}} d x

Multipliziere aus

\frac{3 - 18 x}{1 - 9 x ^{2}} : \frac{3}{1 - 9 x ^{2}} - \frac{18 x}{1 - 9 x ^{2}}

= \int \frac{3}{1 - 9 x ^{2}} - \frac{18 x}{1 - 9 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 - 9 x ^{2}} d x - \int \frac{18 x}{1 - 9 x ^{2}} d x

\int \frac{3}{1 - 9 x ^{2}} d x = arcsin (3 x)

\int \frac{18 x}{1 - 9 x ^{2}} d x = - 2 1 - 9 x^{2}

= arcsin (3 x) - (- 2 1 - 9 x^{2})

Vereinfache

= arcsin (3 x) + 2 1 - 9 x^{2}

Füge eine Konstante zur Lösung hinzu

= arcsin (3 x) + 2 1 - 9 x^{2} + C

Graph

Beliebte Beispiele

derivative of (x+1/(x^3+x+1))

\frac{d}{d x} (\frac{x + 1}{x ^{3} + x + 1})

d/(dt)(1/(t^2+1))

\frac{d}{d t} (\frac{1}{t ^{2} + 1})

tangent f(x)=x+1-ln(x),\at x=0.5

t an g e n t f (x) = x + 1 - ln (x), at x = 0.5

(t^2+x^2)dt+(tx)dx=0

(t^{2} + x^{2}) d t + (t x) d x = 0

derivative of ln(xsqrt(x^2-7))

\frac{d}{d x} (ln (x x^{2} - 7))