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

Lösung

\int 7 x^{6} - \frac{6}{x ^{6}} d x

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

Schritte zur Lösung

\int 7 x^{6} - \frac{6}{x ^{6}} 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 7 x^{6} d x - \int \frac{6}{x ^{6}} d x

\int 7 x^{6} d x = x^{7}

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

= x^{7} - (- \frac{6}{5 x ^{5}})

Vereinfache

= x^{7} + \frac{6}{5 x ^{5}}

Füge eine Konstante zur Lösung hinzu

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

\int 5 + 2 x d x

h \to 0 lim (\frac{( a + h ) - ( a )}{h})

n = 1 \sum \infty (5)^{- n}

\int_{- 3}^{3} sin (x) x d x

\frac{d}{d x} (x^{\frac{9}{2}})