integral 2(sin(x))^3+sin(x)+tan^5(x)

Lösung

integral

2 (sin (x))^{3} + sin (x) + tan^{5} (x)

- 3 cos (x) + \frac{2}{3} cos^{3} (x) + ln ∣ sec (x) ∣ - sec^{2} (x) + \frac{1}{4} sec^{4} (x) + C

Schritte zur Lösung

\int 2 (sin (x))^{3} + sin (x) + tan^{5} (x) d x

Wende die Summenregel an:

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

= \int 2 (sin (x))^{3} d x + \int sin (x) d x + \int tan^{5} (x) d x

\int 2 (sin (x))^{3} d x = 2 (- cos (x) + \frac{cos ^{3} ( x )}{3})

\int sin (x) d x = - cos (x)

\int tan^{5} (x) d x = ln ∣ sec (x) ∣ - sec^{2} (x) + \frac{sec ^{4} ( x )}{4}

= 2 (- cos (x) + \frac{cos ^{3} ( x )}{3}) - cos (x) + ln ∣ sec (x) ∣ - sec^{2} (x) + \frac{sec ^{4} ( x )}{4}

Vereinfache

2 (- cos (x) + \frac{cos ^{3} ( x )}{3}) - cos (x) + ln ∣ sec (x) ∣ - sec^{2} (x) + \frac{sec ^{4} ( x )}{4} : - 3 cos (x) + \frac{2}{3} cos^{3} (x) + ln ∣ sec (x) ∣ - sec^{2} (x) + \frac{1}{4} sec^{4} (x)

= - 3 cos (x) + \frac{2}{3} cos^{3} (x) + ln ∣ sec (x) ∣ - sec^{2} (x) + \frac{1}{4} sec^{4} (x)

Füge eine Konstante zur Lösung hinzu

= - 3 cos (x) + \frac{2}{3} cos^{3} (x) + ln ∣ sec (x) ∣ - sec^{2} (x) + \frac{1}{4} sec^{4} (x) + C

in t e g r a l \frac{x ^{2}}{( 1 + x ^{2} )}

in t e g r a l (1 - n) cos (x)

in t e g r a l \frac{1}{( r - 1 )}

in t e g r a l \frac{cos ( 1 )}{x}

in t e g r a l \frac{1}{( sin ^{2} ( x ) \cdot cos ^{4} ( x ) )}