integral of (tan(x)+sin(x))cos(x)

Lösung

\int (tan (x) + sin (x)) cos (x) d x

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

Schritte zur Lösung

\int (tan (x) + sin (x)) cos (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int 15 sin^{4} (3 x) cos (3 x) d x

\int x^{7} - 6 x + 8 d x

\int \frac{2}{1 + 4 x ^{2}} + ln (8) \cdot 8^{x} d x

\int - \frac{1}{2} y^{2} d y

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