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Beliebt Rechnen >

integral of cot^2(x)csc^4(x)

Lösung

\int cot^{2} (x) csc^{4} (x) d x

Lösung

- \frac{1}{5} cot^{5} (x) - \frac{1}{3} cot^{3} (x) + C

Schritte zur Lösung

\int cot^{2} (x) csc^{4} (x) d x

Trigonometrische Substitution anwenden

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

Entferne die Konstante:

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

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

Multipliziere aus

u^{2} (u^{2} + 1) : u^{4} + u^{2}

= - \int u^{4} + u^{2} d u

Wende die Summenregel an:

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

= - (\int u^{4} d u + \int u^{2} d u)

\int u^{4} d u = \frac{u ^{5}}{5}

\int u^{2} d u = \frac{u ^{3}}{3}

= - (\frac{u ^{5}}{5} + \frac{u ^{3}}{3})

Setze in

u = cot (x)

ein

= - (\frac{cot ^{5} ( x )}{5} + \frac{cot ^{3} ( x )}{3})

Vereinfache

- (\frac{cot ^{5} ( x )}{5} + \frac{cot ^{3} ( x )}{3}) : - \frac{1}{5} cot^{5} (x) - \frac{1}{3} cot^{3} (x)

= - \frac{1}{5} cot^{5} (x) - \frac{1}{3} cot^{3} (x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} cot^{5} (x) - \frac{1}{3} cot^{3} (x) + C

Graph

Beliebte Beispiele

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

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

inverselaplace s/((s^2+16)^2)

in v erse l a pl a ce \frac{s}{( s ^{2} + 16 ) ^{2}}

4y^{''}+6y^'+7y=0

4 y^{^{''}} + 6 y^{^{'}} + 7 y = 0

derivative of sin(e^{2xy}+e^{sin(2xy)})

\frac{d}{d x} (sin (e^{2 x y}) + e^{s i n (2 x y)})

tangent y=sqrt(4x+33),(4,7)

t an g e n t y = 4 x + 33, (4, 7)