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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Graph

Beliebte Beispiele

integral of x^2-3x+8

\int x^{2} - 3 x + 8 d x

slopeintercept (-7,-6),(10,8)

s l o p e in t erce pt (- 7, - 6), (10, 8)

taylor (3x-10)^{4/3}

t a y l or (3 x - 10)^{\frac{4}{3}}

(\partial)/(\partial x)(1+x^4+y^4)

\frac{\partial}{\partial x} (1 + x^{4} + y^{4})

y^'=-y^3,y(0)=-2

y^{^{'}} = - y^{3}, y (0) = - 2