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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

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

Wenn

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

dann

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

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

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

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

Graph

Beliebte Beispiele

derivative of sin(23x)

\frac{d}{d x} (sin (23 x))

derivative of (x^3+2x^2-4/3)

\frac{d}{d x} (\frac{x ^{3} + 2 x ^{2} - 4}{3})

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\int csc^{15} (x) d x

integral from 1 to 5 of 4/(x^2+2x+1)

\int_{1}^{5} \frac{4}{x ^{2} + 2 x + 1} d x

integral of (sin(x))/(cos^3(x))

\int \frac{sin ( x )}{cos ^{3} ( x )} d x