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Beliebt Rechnen >

integral of (2+sin(x))/(sqrt(x))

Lösung

\int \frac{2 + sin ( x )}{x} d x

Lösung

2 (2 x + \frac{π}{2} § (\frac{2}{π} x)) + C

Schritte zur Lösung

\int \frac{2 + sin ( x )}{x} d x

Wende U-Substitution an

= \int 2 (2 + sin (u^{2})) d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int 2 + sin (u^{2}) d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int 2 d u + \int sin (u^{2}) d u)

\int 2 d u = 2 u

\int sin (u^{2}) d u = \frac{π}{2} § (\frac{2}{π} u)

= 2 (2 u + \frac{π}{2} § (\frac{2}{π} u))

Setze in

u = x

ein

= 2 (2 x + \frac{π}{2} § (\frac{2}{π} x))

Füge eine Konstante zur Lösung hinzu

= 2 (2 x + \frac{π}{2} § (\frac{2}{π} x)) + C

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integral of e^{(-x)/(100)}

\int e^{\frac{- x}{100}} d x

integral of sec^2(1-2x)tan^2(1-2x)

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

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\int sin (ln (x^{3})) d x

integral of-9/(x^2)

\int - \frac{9}{x ^{2}} d x

integral of (x+4)(3x-5)

\int (x + 4) (3 x - 5) d x