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

Lösung

\int \frac{x + 2}{( x + 1 ) ^{2}} d x

- \frac{x + 2}{x + 1} + ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{x + 2}{( x + 1 ) ^{2}} d x

Wende die partielle Integration an

= - \frac{x + 2}{x + 1} - \int - \frac{1}{x + 1} d x

\int - \frac{1}{x + 1} d x = - ln ∣ x + 1 ∣

= - \frac{x + 2}{x + 1} - (- ln ∣ x + 1 ∣)

Vereinfache

= - \frac{x + 2}{x + 1} + ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{x + 2}{x + 1} + ln ∣ x + 1 ∣ + C

\int_{0}^{10} 9800 π (10 - y) d y

\frac{d}{d x} ((x^{2} + 1) (x + 5 + \frac{1}{x}))

x \to 0 lim (\frac{ln ( e ^{x} - x )}{x})

\frac{\partial}{\partial x} (\frac{8 x}{x ^{2} + y ^{2}})

\frac{\partial}{\partial b} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})