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Beliebt Rechnen >

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

Lösung

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

Lösung

d (ln ∣ tan (x) + sec (x) ∣ + sin (x)) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

= d \cdot \int (\frac{1}{cos ^{2} ( x )} + 1) cos (x) d x

Multipliziere aus

(\frac{1}{cos ^{2} ( x )} + 1) cos (x) : \frac{1}{cos ( x )} + cos (x)

= d \cdot \int \frac{1}{cos ( x )} + cos (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

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

\int \frac{1}{cos ( x )} d x = ln ∣ tan (x) + sec (x) ∣

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

= d (ln ∣ tan (x) + sec (x) ∣ + sin (x))

Füge eine Konstante zur Lösung hinzu

= d (ln ∣ tan (x) + sec (x) ∣ + sin (x)) + C

Graph

Beliebte Beispiele

integral of x(x-7)^7

\int x (x - 7)^{7} d x

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\int x^{2} + tan (2 x) d x

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\int \frac{1}{4 - 9 θ ^{2}} d θ

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\int \frac{cos ( 5 x )}{e ^{x}} d x