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Beliebt Rechnen >

integral of (sin(θ)-1)/(cos^2(θ))

Lösung

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

Lösung

sec (θ) - tan (θ) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{sin ( θ ) - 1}{cos ^{2} ( θ )} : \frac{sin ( θ )}{cos ^{2} ( θ )} - \frac{1}{cos ^{2} ( θ )}

= \int \frac{sin ( θ )}{cos ^{2} ( θ )} - \frac{1}{cos ^{2} ( θ )} d θ

Wende die Summenregel an:

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

= \int \frac{sin ( θ )}{cos ^{2} ( θ )} d θ - \int \frac{1}{cos ^{2} ( θ )} d θ

\int \frac{sin ( θ )}{cos ^{2} ( θ )} d θ = sec (θ)

\int \frac{1}{cos ^{2} ( θ )} d θ = tan (θ)

= sec (θ) - tan (θ)

Füge eine Konstante zur Lösung hinzu

= sec (θ) - tan (θ) + C

Graph

Beliebte Beispiele

(\partial)/(\partial y)(e^{-xy})

\frac{\partial}{\partial y} (e^{- x y})

(\partial)/(\partial x)(ye^{x/y}-z)

\frac{\partial}{\partial x} (y e^{\frac{x}{y}} - z)

derivative of (x^2/(5+8x))

\frac{d}{d x} (\frac{x ^{2}}{5 + 8 x})

integral of 1/((x-5)(x-3))

\int \frac{1}{( x - 5 ) ( x - 3 )} d x

laplacetransform 3e^{-3t}

l a pl a ce t r an s f or m 3 e^{- 3 t}