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Beliebt Rechnen >

integral of-sin(x)+1/(cos^2(x))

Lösung

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

Lösung

cos (x) + tan (x) + C

Schritte zur Lösung

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

Verwende die grundlegende trigonometrische Identität:

\frac{1}{cos ( x )} = sec (x)

= \int - sin (x) + sec^{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 sin (x) d x + \int sec^{2} (x) d x

\int sin (x) d x = - cos (x)

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

= - (- cos (x)) + tan (x)

Vereinfache

= cos (x) + tan (x)

Füge eine Konstante zur Lösung hinzu

= cos (x) + tan (x) + C

Graph

Beliebte Beispiele

integral of x^2-ln(x^2)+k

\int x^{2} - ln (x^{2}) + k d x

integral from 1 to 5 of 1

\int_{1}^{5} 1 d x

integral of x^2*e^{-ax}

\int x^{2} \cdot e^{- a x} d x

taylor 1/((x-1))

t a y l or \frac{1}{( x - 1 )}

limit as x approaches 2 of ln(x/(x^2-4))

x \to 2 lim (ln (\frac{x}{x ^{2} - 4}))