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Beliebt Rechnen >

(dy)/(dx)=5^xln(5)+2/(x^2+1)

Lösung

\frac{d y}{d x} = 5^{x} ln (5) + \frac{2}{x ^{2} + 1}

Lösung

y = 5^{x} + 2 arctan (x) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = 5^{x} ln (5) + \frac{2}{x ^{2} + 1}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = 5^{x} ln (5) + \frac{2}{x ^{2} + 1}

Wenn

f^{^{'}} (x) = g (x)

dann

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

y = \int 5^{x} ln (5) + \frac{2}{x ^{2} + 1} d x

\int 5^{x} ln (5) + \frac{2}{x ^{2} + 1} d x = 5^{x} + 2 arctan (x) + c_{1}

y = 5^{x} + 2 arctan (x) + c_{1}

Graph

Beliebte Beispiele

t an g e n t X^{5}

y^{^{''}} + 9 y = x e^{x}

integral from 1200 to 1201 of 0.1

\int_{1200}^{1201} 0.1

integral from-5 to 5 of 1/v

\int_{- 5}^{5} \frac{1}{v} d v

integral of e^{3x}*sqrt(e^{3x)-4}

\int e^{3 x} \cdot e^{3 x} - 4 d x