integral of (x^2-15L)/(x+7)

Lösung

\int \frac{x ^{2} - 15 L}{x + 7} d x

\frac{( 7 + x ) ^{2}}{2} - 14 (7 + x) + 49 ln ∣ 7 + x ∣ - 15 L ln ∣ 7 + x ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} - 15 L}{x + 7} d x

Multipliziere aus

\frac{x ^{2} - 15 L}{7 + x} : \frac{x ^{2}}{7 + x} - \frac{15 L}{7 + 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{x ^{2}}{7 + x} d x - \int \frac{15 L}{7 + x} d x

\int \frac{x ^{2}}{7 + x} d x = \frac{( 7 + x ) ^{2}}{2} - 14 (7 + x) + 49 ln ∣ 7 + x ∣

\int \frac{15 L}{7 + x} d x = 15 L ln ∣ 7 + x ∣

= \frac{( 7 + x ) ^{2}}{2} - 14 (7 + x) + 49 ln ∣ 7 + x ∣ - 15 L ln ∣ 7 + x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{( 7 + x ) ^{2}}{2} - 14 (7 + x) + 49 ln ∣ 7 + x ∣ - 15 L ln ∣ 7 + x ∣ + C

d er i v a t i v e \frac{1 - 3 x - x ^{2}}{x ^{2} - 3}

l a pl a ce t r an s f or m 2 t^{3}

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

im pl i c i t \frac{d y}{d x}, tan (x - y) = \frac{y}{1 - x ^{2}}

\int cot (42 x) d x