integral of 7x(x^6-1/7)

Lösung

\int 7 x (x^{6} - \frac{1}{7}) d x

7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \frac{3 x ^{8}}{8}) + C

Schritte zur Lösung

\int 7 x (x^{6} - \frac{1}{7}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int x (x^{6} - \frac{1}{7}) d x

Wende die partielle Integration an

= 7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \int 3 x^{7} d x)

\int 3 x^{7} d x = \frac{3 x ^{8}}{8}

= 7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \frac{3 x ^{8}}{8})

Füge eine Konstante zur Lösung hinzu

= 7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \frac{3 x ^{8}}{8}) + C

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

(x - 3) \frac{d y}{d x} = 4 (x - 3)^{4} + y

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

\int \frac{70}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

x \to 1 + lim (\frac{x + 7}{x + 2})