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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{tan ( x ) - 1} + C

Schritte zur Lösung

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

(cos (x) - sin (x))^{2} = cos^{2} (x) - 2 cos (x) sin (x) + sin^{2} (x)

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

Faktorisiere

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

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

Trigonometrische Substitution anwenden

= \int \frac{1}{( u - 1 ) ^{2}} d u

Wende U-Substitution an

= \int \frac{1}{v ^{2}} d v

Wende die Potenzregel an

= - \frac{1}{v}

Ersetze zurück

= - \frac{1}{tan ( x ) - 1}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{tan ( x ) - 1} + C

Graph

Beliebte Beispiele

derivative of (8x/(x^2+3))

\frac{d}{d x} (\frac{8 x}{x ^{2} + 3})

derivative of [f(x^2)]=x^5

\frac{d}{d x} [f (x^{2})] = x^{5}

(\partial)/(\partial x)(x^2+2xy+3y^4)

\frac{\partial}{\partial x} (x^{2} + 2 x y + 3 y^{4})

integral of 1/(xsqrt(x+1))

\int \frac{1}{x x + 1} d x

derivative y=ln(4/(x^3))

d er i v a t i v e y = ln (\frac{4}{x ^{3}})