integral of (4x+3)/(2x+5)

Lösung

\int \frac{4 x + 3}{2 x + 5} d x

2 x - \frac{7}{2} ln ∣ 2 x + 5 ∣ + C

Schritte zur Lösung

\int \frac{4 x + 3}{2 x + 5} d x

Lange Division

\frac{4 x + 3}{2 x + 5} : 2 - \frac{7}{2 x + 5}

= \int 2 - \frac{7}{2 x + 5} 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 2 d x - \int \frac{7}{2 x + 5} d x

\int 2 d x = 2 x

\int \frac{7}{2 x + 5} d x = \frac{7}{2} ln ∣ 2 x + 5 ∣

= 2 x - \frac{7}{2} ln ∣ 2 x + 5 ∣

Füge eine Konstante zur Lösung hinzu

= 2 x - \frac{7}{2} ln ∣ 2 x + 5 ∣ + C

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

\int x^{2} - 2 x + 10 d x

\int 3 x^{5} y^{3} d y

\int \frac{x}{cos ^{2} ( 4 x ^{2} + \frac{1}{a} )} d x

\int \frac{- 2 x ^{2} + x - 2}{x ^{5} + 2 x ^{3} + x} d x