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Beliebt Rechnen >

integral of (sec(4x)-cot(4x))

Lösung

\int (sec (4 x) - cot (4 x)) d x

Lösung

\frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{1}{4} ln ∣ sin (4 x) ∣ + C

Schritte zur Lösung

\int sec (4 x) - cot (4 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 sec (4 x) d x - \int cot (4 x) d x

\int sec (4 x) d x = \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣

\int cot (4 x) d x = \frac{1}{4} ln ∣ sin (4 x) ∣

= \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{1}{4} ln ∣ sin (4 x) ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{1}{4} ln ∣ sin (4 x) ∣ + C

Graph

Beliebte Beispiele

derivative of sin(2pix)

\frac{d}{d x} (sin (2 π x))

(\partial)/(\partial x)(x^3+y^2)

\frac{\partial}{\partial x} (x^{3} + y^{2})

x^2y^{''}+15xy^'+49y=0

x^{2} y^{^{''}} + 15 x y^{^{'}} + 49 y = 0

inverselaplace 1/(s^2+10.1s+1)

in v erse l a pl a ce \frac{1}{s ^{2} + 10.1 s + 1}

integral of x-2

\int x - 2 d x