de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (4-3x^2)/((3x^2+4)^2)

Lösung

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

Lösung

\frac{x}{2 ( 3 x ^{2} + 4 )} + \frac{1}{8 3} sin (2 arctan (\frac{3}{2} x)) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{4 - 3 x ^{2}}{( 3 x ^{2} + 4 ) ^{2}} : \frac{4}{( 3 x ^{2} + 4 ) ^{2}} - \frac{3 x ^{2}}{( 3 x ^{2} + 4 ) ^{2}}

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

\int \frac{4}{( 3 x ^{2} + 4 ) ^{2}} d x = \frac{1}{4 3} (arctan (\frac{3}{2} x) + \frac{1}{2} sin (2 arctan (\frac{3}{2} x)))

\int \frac{3 x ^{2}}{( 3 x ^{2} + 4 ) ^{2}} d x = \frac{1}{4 3} arctan (\frac{3}{2} x) - \frac{x}{2 ( 4 + 3 x ^{2} )}

= \frac{1}{4 3} (arctan (\frac{3}{2} x) + \frac{1}{2} sin (2 arctan (\frac{3}{2} x))) - (\frac{1}{4 3} arctan (\frac{3}{2} x) - \frac{x}{2 ( 4 + 3 x ^{2} )})

Vereinfache

\frac{1}{4 3} (arctan (\frac{3}{2} x) + \frac{1}{2} sin (2 arctan (\frac{3}{2} x))) - (\frac{1}{4 3} arctan (\frac{3}{2} x) - \frac{x}{2 ( 4 + 3 x ^{2} )}) : \frac{x}{2 ( 3 x ^{2} + 4 )} + \frac{1}{8 3} sin (2 arctan (\frac{3}{2} x))

= \frac{x}{2 ( 3 x ^{2} + 4 )} + \frac{1}{8 3} sin (2 arctan (\frac{3}{2} x))

Füge eine Konstante zur Lösung hinzu

= \frac{x}{2 ( 3 x ^{2} + 4 )} + \frac{1}{8 3} sin (2 arctan (\frac{3}{2} x)) + C

Graph

Beliebte Beispiele

integral of q^2cos(4q)

\int q^{2} cos (4 q) d q

tangent 3x^2+3x-5

t an g e n t 3 x^{2} + 3 x - 5

(\partial}{\partial x}(\frac{2x)/y)

\frac{\partial}{\partial x} (\frac{2 x}{y})

derivative y=x^4e^{3x}

d er i v a t i v e y = x^{4} e^{3 x}

sum from n=5 to infinity of 1/(n^2+n)

n = 5 \sum \infty \frac{1}{n ^{2} + n}