integral of 6x^5-7x^4-9x^2

Lösung

\int 6 x^{5} - 7 x^{4} - 9 x^{2} d x

x^{6} - \frac{7 x ^{5}}{5} - 3 x^{3} + C

Schritte zur Lösung

\int 6 x^{5} - 7 x^{4} - 9 x^{2} 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 6 x^{5} d x - \int 7 x^{4} d x - \int 9 x^{2} d x

\int 6 x^{5} d x = x^{6}

\int 7 x^{4} d x = \frac{7 x ^{5}}{5}

\int 9 x^{2} d x = 3 x^{3}

= x^{6} - \frac{7 x ^{5}}{5} - 3 x^{3}

Füge eine Konstante zur Lösung hinzu

= x^{6} - \frac{7 x ^{5}}{5} - 3 x^{3} + C

\int x + c d x

\int_{0}^{1} \int_{0}^{x} (\frac{6}{7} (x^{2} + x \cdot \frac{y}{2})) d y d x

x \to \infty lim (ln (9 x) - ln (x + 7))

\int \frac{1}{ln ( x ) x} d x

x \to 19 lim (\frac{x - 19}{x ^{2} - 361})