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Beliebt Rechnen >

integral of tan^{1/2}(x)sec^4(x)

Lösung

\int tan^{\frac{1}{2}} (x) sec^{4} (x) d x

Lösung

\frac{2}{3} tan^{\frac{3}{2}} (x) + \frac{2}{7} tan^{\frac{7}{2}} (x) + C

Schritte zur Lösung

\int tan (x) sec^{4} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int (1 + tan^{2} (x)) sec^{2} (x) tan (x) d x

Wende U-Substitution an

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

Multipliziere aus

u (1 + u^{2}) : u + u^{\frac{5}{2}}

= \int u + u^{\frac{5}{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 d u + \int u^{\frac{5}{2}} d u

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

\int u^{\frac{5}{2}} d u = \frac{2}{7} u^{\frac{7}{2}}

= \frac{2}{3} u^{\frac{3}{2}} + \frac{2}{7} u^{\frac{7}{2}}

Setze in

u = tan (x)

ein

= \frac{2}{3} tan^{\frac{3}{2}} (x) + \frac{2}{7} tan^{\frac{7}{2}} (x)

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} tan^{\frac{3}{2}} (x) + \frac{2}{7} tan^{\frac{7}{2}} (x) + C

Graph

Beliebte Beispiele

derivative of 1/3 x^3+x^2

\frac{d}{d x} (\frac{1}{3} x^{3} + x^{2})

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

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

integral of 6/((x-2)(x+4))

\int \frac{6}{( x - 2 ) ( x + 4 )} d x

(\partial)/(\partial x)((3x+4y)^5)

\frac{\partial}{\partial x} ((3 x + 4 y)^{5})

derivative y=(x^5)/(1-x^4)

d er i v a t i v e y = \frac{x ^{5}}{1 - x ^{4}}