de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (3x^2+x)/((6x^3+3x^2)^2)

Lösung

\int \frac{3 x ^{2} + x}{( 6 x ^{3} + 3 x ^{2} ) ^{2}} d x

Lösung

\frac{1}{9 x} - \frac{1}{18 x ^{2}} - \frac{2}{9 ( 2 x + 1 )} + C

Schritte zur Lösung

\int \frac{3 x ^{2} + x}{( 6 x ^{3} + 3 x ^{2} ) ^{2}} d x

Ermittle den Partialbruch von

\frac{3 x ^{2} + x}{( 6 x ^{3} + 3 x ^{2} ) ^{2}} : - \frac{1}{9 x ^{2}} + \frac{1}{9 x ^{3}} + \frac{4}{9 ( 2 x + 1 ) ^{2}}

= \int - \frac{1}{9 x ^{2}} + \frac{1}{9 x ^{3}} + \frac{4}{9 ( 2 x + 1 ) ^{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{1}{9 x ^{2}} d x + \int \frac{1}{9 x ^{3}} d x + \int \frac{4}{9 ( 2 x + 1 ) ^{2}} d x

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

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

\int \frac{4}{9 ( 2 x + 1 ) ^{2}} d x = - \frac{2}{9 ( 2 x + 1 )}

= - (- \frac{1}{9 x}) - \frac{1}{18 x ^{2}} - \frac{2}{9 ( 2 x + 1 )}

Vereinfache

= \frac{1}{9 x} - \frac{1}{18 x ^{2}} - \frac{2}{9 ( 2 x + 1 )}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9 x} - \frac{1}{18 x ^{2}} - \frac{2}{9 ( 2 x + 1 )} + C

Graph

Beliebte Beispiele

integral of (4+9x)/(1+x^2)

\int \frac{4 + 9 x}{1 + x ^{2}} d x

integral of ((2e^x)/(e^{2-5x)})^2

\int (\frac{2 e ^{x}}{e ^{2 - 5 x}})^{2} d x

integral of arccos(z)

\int arccos (z) d z

integral of t/(1+(3t)^4)

\int \frac{t}{1 + ( 3 t ) ^{4}} d t

integral of x^2cos(pi)x

\int x^{2} cos (π) x d x