integral of ((x-4)^3)/(x-3)

Lösung

\int \frac{( x - 4 ) ^{3}}{x - 3} d x

\frac{x ^{3}}{3} - \frac{9 x ^{2}}{2} + 21 x - ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{( x - 4 ) ^{3}}{x - 3} d x

Lange Division

\frac{( x - 4 ) ^{3}}{x - 3} : x^{2} - 9 x + 21 - \frac{1}{x - 3}

= \int x^{2} - 9 x + 21 - \frac{1}{x - 3} 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 x^{2} d x - \int 9 x d x + \int 21 d x - \int \frac{1}{x - 3} d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 21 d x = 21 x

\int \frac{1}{x - 3} d x = ln ∣ x - 3 ∣

= \frac{x ^{3}}{3} - \frac{9 x ^{2}}{2} + 21 x - ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - \frac{9 x ^{2}}{2} + 21 x - ln ∣ x - 3 ∣ + C

in t e g r a l \frac{1}{x - 1}

\int (x^{\frac{2}{5}} + \frac{4}{x} - 16) d x

\int (x^{2} - 4)^{- \frac{3}{2}} d x

\int \frac{( 4 x + 7 )}{x ^{2} - 5 x + 8} d x

\int 1 + x + x^{2} + x^{3} d x