integral of (x-6)sqrt(x+7)

Lösung

\int (x - 6) x + 7 d x

\frac{2}{3} (x - 6) (x + 7)^{\frac{3}{2}} - \frac{4}{15} (x + 7)^{\frac{5}{2}} + C

Schritte zur Lösung

\int (x - 6) x + 7 d x

Wende die partielle Integration an

= \frac{2}{3} (x - 6) (x + 7)^{\frac{3}{2}} - \int \frac{2}{3} (x + 7)^{\frac{3}{2}} d x

\int \frac{2}{3} (x + 7)^{\frac{3}{2}} d x = \frac{4}{15} (x + 7)^{\frac{5}{2}}

= \frac{2}{3} (x - 6) (x + 7)^{\frac{3}{2}} - \frac{4}{15} (x + 7)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} (x - 6) (x + 7)^{\frac{3}{2}} - \frac{4}{15} (x + 7)^{\frac{5}{2}} + C

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

\int \frac{x ^{2} + 2 x + 8}{x ^{4} - 4 x ^{2}} d x

\int_{1}^{2} \frac{- 1 ln ( x )}{x ^{2}} d x

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

\frac{d}{d x} (- x^{3} + 6 x^{2} - 9 x)