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

Lösung

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

- \frac{x ^{2}}{2 ( x + 3 ) ^{2}} + ln ∣ x + 3 ∣ + \frac{3}{x + 3} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - \frac{x}{( x + 3 ) ^{2}} d x = - ln ∣ x + 3 ∣ - \frac{3}{x + 3}

= - \frac{x ^{2}}{2 ( x + 3 ) ^{2}} - (- ln ∣ x + 3 ∣ - \frac{3}{x + 3})

Vereinfache

= - \frac{x ^{2}}{2 ( x + 3 ) ^{2}} + ln ∣ x + 3 ∣ + \frac{3}{x + 3}

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2}}{2 ( x + 3 ) ^{2}} + ln ∣ x + 3 ∣ + \frac{3}{x + 3} + C

\int 6 x^{4} d x

\frac{d v}{d t} + \frac{( v ^{^{'}} \cdot v )}{t} = v^{^{'}} \cdot (\frac{t}{2} - \frac{1}{2})

\frac{d}{d x} (2 x ln (x))

\int \frac{1}{1 + 4 x - 1} d x

t an g e n t y = \frac{5 x}{1 + x ^{2}}, (5, \frac{25}{26})