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Beliebt Rechnen >

integral of tan^3(10x)

Lösung

\int tan^{3} (10 x) d x

Lösung

- \frac{1}{10} ln ∣ sec (10 x) ∣ + \frac{sec ^{2} ( 10 x )}{20} + C

Schritte zur Lösung

\int tan^{3} (10 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int (- 1 + sec^{2} (10 x)) tan (10 x) d x

Wende U-Substitution an

= \int \frac{- 1 + u ^{2}}{10 u} d u

Multipliziere aus

\frac{- 1 + u ^{2}}{10 u} : - \frac{1}{10 u} + \frac{u}{10}

= \int - \frac{1}{10 u} + \frac{u}{10} 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 \frac{1}{10 u} d u + \int \frac{u}{10} d u

\int \frac{1}{10 u} d u = \frac{1}{10} ln ∣ u ∣

\int \frac{u}{10} d u = \frac{u ^{2}}{20}

= - \frac{1}{10} ln ∣ u ∣ + \frac{u ^{2}}{20}

Setze in

u = sec (10 x)

ein

= - \frac{1}{10} ln ∣ sec (10 x) ∣ + \frac{sec ^{2} ( 10 x )}{20}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{10} ln ∣ sec (10 x) ∣ + \frac{sec ^{2} ( 10 x )}{20} + C

Graph

Beliebte Beispiele

integral of (5x-3)/(x^2-2x-3)

\int \frac{5 x - 3}{x ^{2} - 2 x - 3} d x

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derivative of sin(cos(4x))

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

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