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Beliebt Rechnen >

integral of (1/5-2/(x^3)+2x)

Lösung

\int (\frac{1}{5} - \frac{2}{x ^{3}} + 2 x) d x

Lösung

\frac{1}{5} x + \frac{1}{x ^{2}} + x^{2} + C

Schritte zur Lösung

\int \frac{1}{5} - \frac{2}{x ^{3}} + 2 x 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 \frac{1}{5} d x - \int \frac{2}{x ^{3}} d x + \int 2 x d x

\int \frac{1}{5} d x = \frac{1}{5} x

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

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

= \frac{1}{5} x - (- \frac{1}{x ^{2}}) + x^{2}

Vereinfache

= \frac{1}{5} x + \frac{1}{x ^{2}} + x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} x + \frac{1}{x ^{2}} + x^{2} + C

Graph

Beliebte Beispiele

integral of (x^2)/((1-x^2))

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

integral of (2x-1)/(x^3-16x^2-64x)

\int \frac{2 x - 1}{x ^{3} - 16 x ^{2} - 64 x} d x

integral of ((x^2-x))/((1+3x^2-2x^3))

\int \frac{( x ^{2} - x )}{( 1 + 3 x ^{2} - 2 x ^{3} )} d x

integral of x^4+5sqrt(x)

\int x^{4} + 5 x d x

integral of cos(x)cos(2nx)

\int cos (x) cos (2 n x) d x