integral of (6x+7)/(x^2+4x+4)

Lösung

\int \frac{6 x + 7}{x ^{2} + 4 x + 4} d x

6 ln ∣ x + 2 ∣ + \frac{5}{x + 2} + C

Schritte zur Lösung

\int \frac{6 x + 7}{x ^{2} + 4 x + 4} d x

Multipliziere aus

\frac{6 x + 7}{x ^{2} + 4 x + 4} : \frac{6 x}{x ^{2} + 4 x + 4} + \frac{7}{x ^{2} + 4 x + 4}

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{6 x}{x ^{2} + 4 x + 4} d x + \int \frac{7}{x ^{2} + 4 x + 4} d x

\int \frac{6 x}{x ^{2} + 4 x + 4} d x = 6 (ln ∣ x + 2 ∣ + \frac{2}{x + 2})

\int \frac{7}{x ^{2} + 4 x + 4} d x = - \frac{7}{x + 2}

= 6 (ln ∣ x + 2 ∣ + \frac{2}{x + 2}) - \frac{7}{x + 2}

Vereinfache

6 (ln ∣ x + 2 ∣ + \frac{2}{x + 2}) - \frac{7}{x + 2} : 6 ln ∣ x + 2 ∣ + \frac{5}{x + 2}

= 6 ln ∣ x + 2 ∣ + \frac{5}{x + 2}

Füge eine Konstante zur Lösung hinzu

= 6 ln ∣ x + 2 ∣ + \frac{5}{x + 2} + C

\int_{- 3}^{1} x^{2} e^{x^{3} + 27} d x

in v erse l a pl a ce \frac{( 3 s + 3 )}{s ^{2} - 9}

\int cos^{3} (6 x) d x

a re a x + y = 0, x + y^{2} = 56

s im pl i f y x^{n}