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Beliebt Rechnen >

integral of (5/2)^2+sqrt(x)-cos(5x)

Lösung

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

Lösung

\frac{25}{4} x + \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{5} sin (5 x) + C

Schritte zur Lösung

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

\int (\frac{5}{2})^{2} d x = \frac{25}{4} x

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

\int cos (5 x) d x = \frac{1}{5} sin (5 x)

= \frac{25}{4} x + \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{5} sin (5 x)

Füge eine Konstante zur Lösung hinzu

= \frac{25}{4} x + \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{5} sin (5 x) + C

Graph

Beliebte Beispiele

integral of 1/(9sec(x))

\int \frac{1}{9 sec ( x )} d x

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\int x 5 x^{2} - 2 d x

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\int - \frac{5}{x ln ( x ^{3} )} d x

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

integral of (3+xsqrt(x))

\int (3 + x x) d x